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
(a) 49/4
(b) 4/49
(c) 4
(d) none of these

Answer 1

(a) 49/4

It is given that, 4 is the root of the equation $x^2+px+12=0$.

$$\begin{gathered} \therefore 16+4p+12=0 \\ \Rightarrow p=-7 \end{gathered}$$

It is also given that, the equation $x^2+px+q=0$ has equal roots. So, the discriminant of
$x^2+px+q=0$ will be zero.

$$\begin{gathered} \therefore p^2-4q=0 \\ \Rightarrow 4q={\left(-7\right)}^2=49 \\ \Rightarrow q=\frac{49}{4} \end{gathered}$$