How to find a real positive root of a bi-quadratic equation

Suppose a bi-quadratic equation x^4+4*x^2-7=0. How to find a positive real root of it.

solve(x^4+4*x^2-7=0, x, Real, Positive)

Is the above correct?

How to use fsolve here?

Answer 1

[Matt J]

Why not just use ROOTS?

    >> roots([1 0 4 -7])

    ans =

      -0.6277 + 2.2764i
      -0.6277 - 2.2764i
       1.2554

[Atom]

I just need its positive root and to be assigned it as, say sol and use it in a loop. I use this programme for a complicated 4th degree equation depending on several parameters. I have to vary the parameters very time. It is not possible to see every time the all roots and then to choose the positive one. I just use for loop before finding the roots.

[Matt J]

It is not possible to see every time the all roots and then to choose the positive one.

Why not? That's exactly what the ROOTS command allows you to do.

[Atom]

No no. You are right. From your process, roots can be obtained. But we then have to write codes to find a positive root. Because, suppose, I have a bi-quadratic with one varied parameter. If I change that parameter 100 times, I get 100 equations each of which will give four root & each time I have to find the positive real one. Its a tedious job.

I want to write a code so that I can get the +ve real root easily (supposing the change of parameter that I have discussed herein above)

[Matt J]

OK, then

 sol=roots([1 0 4 -7]);
 sol=sol(imag(sol)==0 & sol>=0);

[Joel Mathew]

Thank you this worked for me