Question

Find the sum of square of the roots $(\sum x_1^2)$ of biquadratic equation $x^4+2g{x}^3+d{x}^2+2f{c}^{2}x+c^4=0$ if $x_1.x_2.x_3.x_4$ are the roots of the equation.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given biquadratic equation is,

$x^4+2g{x}^3+d{x}^2+2f{c}^{2}x+c^4=0$ - - - - - - - (1)

$\sum x_1^2=(x_1^2+x_2^2+x_3^2+x_4^2)$

=$(x_1+x_2+x_3+x_4{)}^2-2\sum x_1{x}_2$

sum of the roots of equation (1) = $\frac{-2g}{1}=-2g$

sum of the roots taking two at a time = $\frac{d}{1}=d$

=$(-2g{)}^2-2(d)=4g^2-2d$