Finding all roots to equation [duplicate]











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  • About multi-root search in Mathematica for transcendental equations

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I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:



enter image description here



The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?



Thanks in advance.






plotting equation-solving







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marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
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This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.
    – Michael E2
    16 hours ago










  • @MichaelE2 - I would guess that NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
    – Bob Hanlon
    9 hours ago












  • @BobHanlon You can see in the comments to @zhk's answer below that NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
    – Michael E2
    8 hours ago















up vote
2
down vote

favorite













This question already has an answer here:




  • About multi-root search in Mathematica for transcendental equations

    8 answers




I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:



enter image description here



The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?



Thanks in advance.






plotting equation-solving







share|improve this question













marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
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 13 hours ago


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.
    – Michael E2
    16 hours ago










  • @MichaelE2 - I would guess that NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
    – Bob Hanlon
    9 hours ago












  • @BobHanlon You can see in the comments to @zhk's answer below that NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
    – Michael E2
    8 hours ago













up vote
2
down vote

favorite









up vote
2
down vote

favorite












This question already has an answer here:




  • About multi-root search in Mathematica for transcendental equations

    8 answers




I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:



enter image description here



The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?



Thanks in advance.






plotting equation-solving







share|improve this question














This question already has an answer here:




  • About multi-root search in Mathematica for transcendental equations

    8 answers




I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:



enter image description here



The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?



Thanks in advance.





This question already has an answer here:




  • About multi-root search in Mathematica for transcendental equations

    8 answers







plotting equation-solving




plotting equation-solving






share|improve this question













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asked 21 hours ago









wznd

182




182




marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
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  • Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.
    – Michael E2
    16 hours ago










  • @MichaelE2 - I would guess that NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
    – Bob Hanlon
    9 hours ago












  • @BobHanlon You can see in the comments to @zhk's answer below that NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
    – Michael E2
    8 hours ago


















  • Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.
    – Michael E2
    16 hours ago










  • @MichaelE2 - I would guess that NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
    – Bob Hanlon
    9 hours ago












  • @BobHanlon You can see in the comments to @zhk's answer below that NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
    – Michael E2
    8 hours ago
















Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.
– Michael E2
16 hours ago




Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.
– Michael E2
16 hours ago












@MichaelE2 - I would guess that NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
– Bob Hanlon
9 hours ago






@MichaelE2 - I would guess that NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
– Bob Hanlon
9 hours ago














@BobHanlon You can see in the comments to @zhk's answer below that NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
– Michael E2
8 hours ago




@BobHanlon You can see in the comments to @zhk's answer below that NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
– Michael E2
8 hours ago










1 Answer
1






active

oldest

votes

















up vote
5
down vote













You can use NSolve to find multiple roots,



NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}




or FindAllCrossings from here,



FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10}, 

 WorkingPrecision -> 20]



{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}




or FindRoot providing good initial guesses, 



FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}







share|improve this answer























  • When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
    – wznd
    19 hours ago












  • @wznd You should input the interval of interest.
    – zhk
    19 hours ago










  • @wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
    – Mariusz Iwaniuk
    19 hours ago






  • 1




    @MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
    – Mariusz Iwaniuk
    17 hours ago








  • 1




    @MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
    – zhk
    17 hours ago




















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
5
down vote













You can use NSolve to find multiple roots,



NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}




or FindAllCrossings from here,



FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10}, 

 WorkingPrecision -> 20]



{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}




or FindRoot providing good initial guesses, 



FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}







share|improve this answer























  • When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
    – wznd
    19 hours ago












  • @wznd You should input the interval of interest.
    – zhk
    19 hours ago










  • @wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
    – Mariusz Iwaniuk
    19 hours ago






  • 1




    @MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
    – Mariusz Iwaniuk
    17 hours ago








  • 1




    @MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
    – zhk
    17 hours ago

















up vote
5
down vote













You can use NSolve to find multiple roots,



NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}




or FindAllCrossings from here,



FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10}, 

 WorkingPrecision -> 20]



{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}




or FindRoot providing good initial guesses, 



FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}







share|improve this answer























  • When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
    – wznd
    19 hours ago












  • @wznd You should input the interval of interest.
    – zhk
    19 hours ago










  • @wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
    – Mariusz Iwaniuk
    19 hours ago






  • 1




    @MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
    – Mariusz Iwaniuk
    17 hours ago








  • 1




    @MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
    – zhk
    17 hours ago















up vote
5
down vote










up vote
5
down vote









You can use NSolve to find multiple roots,



NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}




or FindAllCrossings from here,



FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10}, 

 WorkingPrecision -> 20]



{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}




or FindRoot providing good initial guesses, 



FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}







share|improve this answer














You can use NSolve to find multiple roots,



NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}




or FindAllCrossings from here,



FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10}, 

 WorkingPrecision -> 20]



{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}




or FindRoot providing good initial guesses, 



FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}



{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}








share|improve this answer














share|improve this answer



share|improve this answer








edited 19 hours ago

























answered 19 hours ago









zhk

8,64911433




8,64911433












  • When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
    – wznd
    19 hours ago












  • @wznd You should input the interval of interest.
    – zhk
    19 hours ago










  • @wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
    – Mariusz Iwaniuk
    19 hours ago






  • 1




    @MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
    – Mariusz Iwaniuk
    17 hours ago








  • 1




    @MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
    – zhk
    17 hours ago




















  • When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
    – wznd
    19 hours ago












  • @wznd You should input the interval of interest.
    – zhk
    19 hours ago










  • @wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
    – Mariusz Iwaniuk
    19 hours ago






  • 1




    @MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
    – Mariusz Iwaniuk
    17 hours ago








  • 1




    @MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
    – zhk
    17 hours ago


















When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago






When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago














@wznd You should input the interval of interest.
– zhk
19 hours ago




@wznd You should input the interval of interest.
– zhk
19 hours ago












@wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
– Mariusz Iwaniuk
19 hours ago




@wznd. For me NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.
– Mariusz Iwaniuk
19 hours ago




1




1




@MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago






@MichaelE2. With little modification works on MMA 11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago






1




1




@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago






@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago





-

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