Question

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

• A. $\frac{4}{49}$
• B. $\frac{49}{4}$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

Answer: (B)

Given, 4 is a root of the equation
$x^2+px+12=0$
$\therefore$ $16+4p+12=0$
$\Rightarrow$ $4p=-28$
$\Rightarrow$ $p=-7$
And equation $x^2+px+q=0$
have equal roots, let roots are
$\alpha ,\alpha$ .
$\therefore$ $\alpha +\alpha =-\frac{p}{1}=-p$
$\Rightarrow$ $2\alpha =-p$
$\Rightarrow$ $\alpha =-\frac{p}{2}=\frac{7}{2}$
$[\because p=-7]$ and $\alpha .\alpha =q$
$\Rightarrow$ ${\left(\frac{7}{2}\right)}^2=q$
$\Rightarrow$ $q=\frac{49}{4}$