If α and β are the roots of the equation ax 2+ bx + c =0 then the sum of the roots of the equation a2 x2+(b2-2 a c) x+b2-4 a c=0 in terms of α and β is given by

Question

If α and β are the roots of the equation ax 2+ bx + c =0 then the sum of the roots of the equation a2 x2+(b2-2 a c) x+b2-4 a c=0 in terms of α and β is given by (A) -(α2-β2) (B) (α+β)2-2 α β (C) α2 β+β α2-4 α β (D) -(α2+β2)

Tardigrade Admin · Accepted Answer

α+β=-( b / a ) ; α β=( c / a ) ; x 1+ x 2=(2 ac - b 2/ a 2)=(2 c / a )-(( b / a ))2=2 α β-(α+β)2=-(α2+β2.

Q. If $α$ and $β$ are the roots of the equation $a x^{2} + b x + c = 0$ then the sum of the roots of the equation $a^{2} x^{2} + (b^{2} - 2 a c) x + b^{2} - 4 a c = 0$ in terms of $α$ and $β$ is given by

$- (α^{2} - β^{2})$

$(α + β)^{2} - 2 α β$

$α^{2} β + β α^{2} - 4 α β$

$- (α^{2} + β^{2})$

$α + β = - \frac{b}{a}; α β = \frac{c}{a}; x_{1} + x_{2} = \frac{2 a c - b ^{2}}{a ^{2}} = \frac{2 c}{a} - (\frac{b}{a})^{2} = 2 α β - (α + β)^{2} = - (α^{2} + β^{2}$

Q. If α and β are the roots of the equation ax2+bx+c=0 then the sum of the roots of the equation a2x2+(b2−2ac)x+b2−4ac=0 in terms of α and β is given by

−(α2−β2)

(α+β)2−2αβ

α2β+βα2−4αβ

−(α2+β2)