Question

If one of the roots of the quadratic equation $x^2+3x+k=0$ is $3$, then find the other root.

• A. $-18$
• B. $18$
• C. $-6$
• D. $6$

Answer 1

The correct option is C $-6$

We know that if $\alpha$ is the root of an equation $a{x}^2+bx+c=0$, then $a{\alpha }^2+b\alpha +c=0$.

Substituting $x=3$ in the equation $x^2+3x+k=0$, we get,
$⟹3^2+3\left(3\right)+k=0$
$⟹k=-18$
The given equation $x^2+3x-18=0$ becomes:
$⟹x^2+6x-3x-18=0$
$⟹x(x+6)-3(x+6)=0$
$⟹(x+6)(x-3)=0$
$⟹(x+6)=0$ or $(x-3)=0$
$⟹x=-6$ or $x=3$
So, $-6$ and $3$ are the roots of the given quadratic equation.
$\therefore -6$ is the other root.