If one root of the equation x
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.

$\therefore p^{2}-4 q=0$

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

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