Question

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

Options

•  49/4

•  4/49

• 4

• none of these

Answer 1

49/4
It is given that, 4 is the root of the equation \[x^2 + px + 12 = 0\].

\[\therefore 16 + 4p + 12 = 0\]

\[ \Rightarrow p = - 7\]

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.

\[\therefore p^2 - 4q = 0\]

\[ \Rightarrow 4q = \left( - 7 \right)^2 = 49\]

\[ \Rightarrow q = \frac{49}{4}\]