SOLUTION: Find the quadratic equation with roots which are the squares of the roots of x^2 -5x -3 =0

Question 285937: Find the quadratic equation with roots which are the squares of the roots of
x^2 -5x -3 =0
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x^2 -5x -3 =0
x^2 -5x =3
(5/2)^2=25/4
3=12/4
x^2-5x+25/4=3+25/4
(x-5/2)^2=37/4
x=5/2-sqrt(37/4)
x=5/2+sqrt(37/4)
c=1/2(5-sqrt(37))
d=1/2(5+sqrt(37))

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=37 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.54138126514911, -0.54138126514911. Here's your graph:

let's call the roots c and d
so the new equation will have x^2 and y^2 as there roots
(a-c^2)*(b-d^2)=0
ab-bc^2-ad^2+c^2d^2=0
plug these in .
c=1/2(5-sqrt(37))
d=1/2(5+sqrt(37))

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