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)

$\frac{49}{4}$

Since, $4$ is a root of $x^2+ax+12=0$ ..... $\left(i\right)$

$\therefore 16+4a+12=0$

$\Rightarrow a=-7$

Let the roots of the equation $x^2+ax+b=0$ .... $\left(ii\right)$ be $\alpha$ and $\alpha$ .

$\therefore 2\alpha =-a$

$\Rightarrow \alpha =\frac{7}{2}$

and $\alpha .\alpha =b$

$\Rightarrow {\alpha }^2=b$

$\Rightarrow {\left(\frac{7}{2}\right)}^2=b$

$\Rightarrow b=\frac{49}{4}$