Question

If one root of the equation $x^2+px+12=0$~is~4,while the equation

$x^2+px+q=0$ has equal roots, the value of q is

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

Answer 1

The correct option is A

$\frac{49}{4}$

It is given that, 4 is the root of the equation

$x^2+px+12=0\therefore 16+4p+12=0\Rightarrow p=-7$

It is also given that, the equation$x^2+px+q=0$has equal roots. So, the discriminant of$x^2+px+q=0$ will be zero. $\therefore p^2-4q=0\Rightarrow 4q=(-7{)}^2=49\Rightarrow q=\frac{49}{4}$