Question

If one root of the equation $x^2+px+12=0$ is 4, while the roots of the equation $x^2+px+q=0$ are same, then the value of q will be

• A. $\frac{4}{49}$
• B. None of these
• C. $4$
• D. $\frac{49}{4}$

Answer 1

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

Given: $x=4$ is a root of $x^2+px+12=0$.
Put $x=4$ in $x^2+px+12=0,$
$\Rightarrow p=-7$

Now second equation $x^2+px+q=0$ have equal roots.
Let the root be $r$.
Sum of roots: $r+r=-p,$
Product of roots: $r^2=q$
Therefore $p^2=4q\Rightarrow q=\frac{49}{4}$