Question

If the sum of roots of $a{x}^2+bx+c=0$ is equal to sum of the square of their reciprocal, then find the value of $\frac{b^2}{ac}+\frac{bc}{a^2}$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$a{x}^2+bx+c=0$

$\alpha +\beta =\frac{1}{{\alpha }^2}+\frac{1}{{\beta }^2}=\frac{-b}{a}$

Let, $P=\alpha$, $Q=\beta$

$⟹\frac{-b}{a}=\frac{(P+Q{)}^2-2PQ}{P^2{Q}^2}$

$⟹\frac{-b}{a}=\frac{(\frac{b^2}{a^2}-2\frac{c}{a})}{c^2/a^2}$

$⟹2c{a}^2=b^{2}a+b{c}^2$

$⟹2=\frac{b^2}{ac}+bc{a}^2$