Question

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

• A. $\frac{49}{4}$
• B. $12$
• C. $3$
• D. $4$

Answer 1

The correct option is A $\frac{49}{4}$

Since $4$ is one of the roots of equation $x^2+px+12=0$ so it must satisfy the equation.
$\therefore 16+4p+12=0\Rightarrow 4p=-28\Rightarrow p=-7$
The other equation is $x^2-7x+q=0$ whose roots are equal.
Let the root be $\alpha$
Therefore sum of roots $\alpha +\alpha =\frac{7}{1}\Rightarrow 2\alpha =7\Rightarrow \alpha =\frac{7}{2}$
and product of roots $\alpha .\alpha =q\Rightarrow {\alpha }^2=q\Rightarrow q=\frac{49}{4}$.