Question

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

Answer 1

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

Let's put $x=4in{x}^2+px+12=0,$ which gets us $p=-7$
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 $p^2=4q\Rightarrow q=\frac{49}{4}$