Question

the roots of Ax^2+Bx+C=0 are r and s . for the roots of x^2+px+q =0 to be r^2 and s^2, what must be the value of p ?

Answer 1

Given: rands are roots of ax2+bx+c=o

⇒r+s=−ba

and rs=ca

r2+s2=(r+s)2−2rs

=b2a2−

2ca=b2−2aca2

r2s2=c2a2

Quadratic Eqn., whose roots are r2ands2

is

x2−(r2+s2)x+r2s2

=x2−(b2−2aca2)

x+c2a2

Given: x2+px+q=0

is equation whose roots are r2ands2

⇒p=−b2−2aca2=2ac−b2a2