Question

If the roots of the equation $x^2+px-6=0$ are $6$ and $-1$ then the value of $p$ is

• A. $2$
• B. $3$
• C. $-5$
• D. $5$

Answer 1

The correct option is C $-5$

GIven equation is :

$x^2+px-6=0$ ...... $\left(i\right)$

$6$ and $-1$ are the roots of $\left(i\right)$

So, they satisfies $\left(i\right)$

If $6$ is the root of $\left(i\right)$

$⟹(6{)}^2+p(6)-6=0\Rightarrow 36+6p-6=0\Rightarrow 6p=-36+6\Rightarrow 6p=-30\Rightarrow p=-5$

If the root is $-1$ then

$(-1{)}^2+p(-1)-6=0\Rightarrow 1-p-6=0\Rightarrow -p=6-1\Rightarrow p=-5$

$\therefore p=-5$

Alternate Method

$6$ and $-1$ are the roots of $\left(i\right)$

$⟹(x-6)(x+1)=x^2+px-6$

$⟹x^2+x-6x-6=x^2+px-6$

$⟹x^2-5x-6=x^2+px-6$

$⟹p=-5$