Express through p and q the sum of the squares of the roots of the equation x2+px+q=0.

Question

 I need this asap because this is important

Answer 1

you can use the quadratic formula

(-p±√(p²-4q))/2

(-p+√(p²-4q))/2 and (-p-√(p²-4q))/2

square both roots to get...

(p²-2p√(p²-4q)+p²-4q)/4

(p²+2p√(p²-4q)+p²-4q)/4

add them together and the radicals will cancel and you get...

(4p²-8q)/4=p²-2q

Answer 2

It's p² - 2q. Let s and t be roots of the polynomial x² + px + q. Then s + t = -p and st = q. So the sum of the squares of the roots is s² + t², which is the same as

 

(s² + 2st + t²) - 2st = (s + t)² - 2st = (-p)² - 2q = p² - 2q