Question

lf the roots of equation $x^2+bx+ac=0$ are $\alpha$ and $\beta$, the roots of the equation $x^2+ax+bc=0$ are $\alpha$ and $\gamma$, then the values of $\alpha ,\beta ,\gamma$ are respectively

• A. $c,b,a$
• B. $c,a,b$
• C. $a,c,b$
• D. $b,a,c$

Answer 1

Answer: (B)

$c,a,b$

$\alpha +\beta =-b$
$\alpha \beta =ac$
Similarly,
$\alpha +\gamma =-a$
$\alpha \gamma =bc$
Now $\alpha$ is the common root.
Therefore, from the equations,
$\alpha \beta =ac$ and $\alpha \gamma =bc$
We get the common root $\alpha =c$
Therefore
$\beta =a$ and $\gamma =b$
Since $\alpha +\beta =-b$
Hence
$c+a=-b$
$a+b+c=0$