Question

The sum of the roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of the squares of their reciprocals, then $b{c}^2,c{a}^2,a{b}^2$ are in

• A. A. P.
• B. G. P.
• C. H. P.
• D. None of these

Answer 1

The correct option is A A. P.

$\alpha +\beta =\frac{1}{{\alpha }^2}+\frac{1}{{\beta }^2}$
$\alpha +\beta =\frac{(\alpha +\beta {)}^2-2\alpha \beta }{{\alpha }^2{\beta }^2}$
Substitute the values
$\alpha +\beta =\frac{-b}{a},\alpha \beta =\frac{c}{a}$, then we will get
$-b{c}^2-a{b}^2=2a^{2}b$
So,
$-b{c}^2,a^{2}b,-a{b}^2$ are in A.P
Hence, option 'A' is correct.