# My code is giving only one solution to a function although there are two solutions, what can I do to get all the solutions?

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f(t) = 1.4*exp(0.5*x)-2*x-3 = 0 is the function I tried to solve. Here the variable t indicates time. From plotting the graph I know that there are two roots, one is positive and the other negative. But my code is giving only the negative root which I actually don't need. What should I do to get both the roots?
My Code:
syms x
y2 = 1.4*exp(0.5*x)-2*x-3;
g = y2 == 0;
roots = vpa(solve(y2,x))

David Goodmanson on 15 Jun 2022
Edited: David Goodmanson on 15 Jun 2022
Hi JN,
syms x; assume(x,'positive')
and proceed as before for the second one.
It is not a great idea to use 'roots' as the name of a variable, since it is the name of a Matlab function.

Walter Roberson on 16 Jun 2022
vpasolve(y2,x, [0 inf] )
Walter Roberson on 18 Jun 2022
If you have a function with two roots and they are known to be at least Delta apart but you do not know the order, then
• vpasolve once, getting first root
• vpasolve a second time with range -inf to first minus Delta/2. If you got an answer it is the second root.
• If you did not get an answer then vpasolve range first plus Delta/2 to infinity. If you got an answer it is the second root
• If you did not get an answer earlier second time then perhaps there are not two roots, or perhaps they are closer together than Delta, or perhaps Delta is insignificant compared to the location of the root, or perhaps the equations are too steep for vpasolve, or perhaps the Newton-Raphson projection for a point inside the barrier was outside the barrier in which case vpasolve gives up.

R2020a

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