Question

If a root of the equations $x^2-px-12=0$ is 4, While the roots of the equations $x^2+px+q=0$ are same, then the value of q will be

• A. $4$
• B. $\frac{4}{3}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{4}$

$\Rightarrow$ One root of $x^2-px-12=0$ is $4$

$\Rightarrow$ Then substituting $x=4$

$\Rightarrow$ $(4{)}^2-p(4)-12=0$

$\Rightarrow$ $16-4p-12=0$

$\Rightarrow$ $4p=4$

$\therefore$ $p=1$

$\Rightarrow$ $x^2+px+q=0$ has equal roots.

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

$\Rightarrow$ $(1{)}^2-4q=0$

$\Rightarrow$ $1=4q$

$\therefore$ $q=\frac{1}{4}$