Question

If one root of equation $ x^2 + ax + 12 = 0 $ is $ 4 $ while the equation $ x^2 + ax + b = 0 $ has equal roots, then the value of $ b $ is

• A. $ \frac{4}{49} $
• B. $ \frac{49}{4} $
• C. $ \frac{7}{4} $
• D. $ \frac{4}{7} $

Answer 1

Answer: (B)

Since, $4$ is a root of $x^{2}+a x+12=0$
$\therefore 16+4 a+12=0$
$ \Rightarrow a=-7$
Let the roots of the equation $x^{2}+a x+b=0$ be $\alpha$ and $\alpha$.
$\therefore 2 \alpha=-a $
$\Rightarrow \alpha=\frac{7}{2}$
and $\alpha \cdot \alpha=b$
$ \Rightarrow \left(\frac{7}{2}\right)^{2}=b$
$\Rightarrow b=\frac{49}{4}$