Question

If $-4$ is a root of the equation $x^2+px-4=0$ and the equation $x^2+px+q=0$ has equal roots, then the values of $p$ and $q$ are, respectively

• A. $-3$ and $\frac{9}{4}$
• B. $3$ and $\frac{9}{4}$
• C. $\frac{9}{4}$ and $3$
• D. $4$ and $3$

Answer 1

The correct option is B $3$ and $\frac{9}{4}$

Given $x=-4$ is a root of the equation

$f\left(x\right)=x^2+px-4$

$\therefore$ $f(x=-4)=0$

$\Rightarrow 16-4p-4=0$

$\Rightarrow 12-4p=0$

$\Rightarrow p=3$

Also the equation,

$x^2+px+q=0$ has double roots

$\Rightarrow$ Discriminant $=0$

$\Rightarrow p^2-4q=0$

$\Rightarrow 9-4q=0$

$\Rightarrow q=9/4$

$\therefore$ $p=3$ & $q=9/4$

Option B.