How to find only positive root of a polynomial

How to find only positive root of a polynomial equation x^4+7*x^2-A=0 where A is varying from 1:.1:3. If rr is the positive real root, then find rr/(rr+1) for each case.

for A=1:.1:3
poly = [1 0 7 0 A];
R = roots(poly);
if isa(R,'complex') && (R<=0)
 continue;
 else
R/(R+1)
end
Please correct the code.

[Matt J]

What do you mean by "without solving a polynomial equation"? A root is, by definition, the solution to such a problem.

[Atom]

Yes. you are right. Please ignore the words "without solving".

Answer 1

[Matt J]

By the quadratic formula, the largest solution for x^2 is

x^2 = (-7+ sqrt(49+4*A))/2

For positive A, this will always be positive. You can then get a positive root for x by doing

x = sqrt( (-7+ sqrt(49+4*A))/2 )

I don't know if this satisfies your requirement "without solving a polynomial equation". It doesn't seem possible that you meant this literally (see my comment above).

[Atom]

Please ignore the words "without solving". Please modify the above code so that I can use it for general one.

[Matt J]

for A=1:.1:3

    b=poly(3);
    a=poly(1);

    R = sqrt( (-b+ sqrt(b^2+4*A*a))/2/a );

    R/(R+1)

end