If € , ß are the roots of the equation

Question

2x^2 + 4x - 3 = 0 and €^2 , ß^2 are the roots of the equation x^2 + px + q = 0, find the value of p.

Answer 1

Recall that for a given quadratic equation,
x^2 - (sum of roots)x + (product of roots)

we can rewrite the first quadratic eqn as
x^2 + 2x - 3/2 = 0
Therefore, sum of roots is -2 and their product is -3/2, or
€ + ß = -2
ۧ = -3/2

Since were looking for p (which is the sum of roots, €^2 and ß^2, for the 2nd equation given), we can make an expression for p:
-p = €^2 + ß^2
p = -(€^2 + ß^2)

Note that
€^2 + ß^2 = (€ + ß)^2 - 2€ß
Thus we can substitute values:
€^2 + ß^2 = (-2)^2 - 2(-3/2)
€^2 + ß^2 = ?

Now solve for it, and don't forget to multiply it by -1 since we're looking for p, not -p.
Hope this helps~ :3