Question

if alpha beta are the roots of the equation ax ^2 + bx + c =0 then the roots of the equation (a + b + c) x ^2 -( b + 2 c) x + c = 0 are

Answer 1

Hey..

Equation ax2+bx+c=0 has roots α and β

α+β=−ba

αβ=ca

Equation Ax2+Bx+C=0 has roots α3 and β3

CA=α3β3=(αβ)3=c3a3

BA=−(α3+β3)=3αβ(α+β)−(α+β)3=3(ca)(−ba)−(−ba)3=b3−3abca3

A=a3,B=b3−3abc,C=c3

Quadratic equation with roots α3 and β3:

a3x2+b(b2−3ac)x+c3=0

See