Question

If the roots of the equation $x^2+bx+ac=0are\alpha ,\beta$ and roots of the equation $x^2+ax+bc=0$ are $\alpha ,\gamma$ then the value of $\alpha ,\beta ,\gamma$ respectively (Previous year JEE question)

• A. a, b, c
• B. b, c, a
• C. c, a, b
• D. None of these

Answer 1

The correct option is C c, a, b

$\alpha +\beta =-b...\left(1\right)$
$\alpha \beta =ac...\left(2\right)$
$\alpha +\gamma =-a...\left(3\right)$
$\alpha \gamma =bc...\left(4\right)$
$\left(1\right)-\left(3\right)\Rightarrow \beta -\gamma =a-b...\left(5\right)$
$\frac{\left(2\right)}{\left(4\right)}\Rightarrow \frac{\beta }{\gamma }=\frac{a}{b}$
$\beta =\frac{a\gamma }{b}...\left(6\right)$
putting the value of $\beta$ in (5)
$\frac{a\gamma }{b}-\gamma =a-b\Rightarrow \gamma \frac{(a-b)}{b}=(a-b)\therefore \gamma =b\therefore \beta =aand\alpha =c$