Question

For what value of 'a' will the roots the roots of the equation:$3x^2+(7+a)x+(8-a)=0$ be equal ?

Answer 1

The roots of a quadratic equation are equal if its discriminant is 0.
$(7+a{)}^2-4(3\left)\right(8-a)=0$
$⟹49+14a+a^2-96+12a=0$
$⟹a^2+26a-47=0$
$⟹a=\frac{-26\pm \sqrt{{26}^2-4\cdot (-47)}}{2}=\frac{-26\pm \sqrt{864}}{2}$
$⟹a=-13\pm \sqrt{216}$