Question

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

Answer 1

Given: $4$ is one root of the equation $x^2+px+12=0$, then

$4^2+p\left(4\right)+12=0$

$\Rightarrow 4p+28=0$

$\therefore p=-7\dots \left(1\right)$

Also, $x^2+px+q=0$ has equal roots

$D=0$

$\Rightarrow b^2-4ac=0$

$\Rightarrow p^2-4\left(1\right)\left(q\right)=0$

$\Rightarrow q=\frac{p^2}{4}$

From equation $\left(1\right)$, we get

$\Rightarrow q=\frac{(-7{)}^2}{4}=\frac{49}{4}$

Hence, Option (A) is correct.