Question:
If one root of the equation $x^{2}+p x+12=0$ is 4 , while the equation $x^{2}+p x+q=0$ has equal roots, the value of $q$ is
(a) 49/4
(b) 4/49
(c) 4
(d) none of these
Solution:
(a) 49/4
It is given that, 4 is the root of the equation $x^{2}+p x+12=0$.
$\therefore 16+4 p+12=0$
$\Rightarrow p=-7$
It is also given that, the equation $x^{2}+p x+q=0$ has equal roots. So, the discriminant of $x^{2}+p x+q=0$ will be zero.
$\therefore p^{2}-4 q=0$
$\Rightarrow 4 q=(-7)^{2}=49$
$\Rightarrow q=\frac{49}{4}$