Question

Question 1 (iii)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$-3x^2+5x+12=0$

Answer 1

Given equation is $-3x^2+5x+12=0$
on comparing with $a{x}^2$ + bx + c = 0, we get
a = - 3, b = 5 and c = 12
by quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$=\frac{-\left(5\right)\pm \sqrt{(5{)}^2-4(-3\left)\right(12)}}{2(-3)}$
$=\frac{-5\pm \sqrt{25+144}}{-6}=\frac{-5\pm \sqrt{169}}{-6}$
$=\frac{-5\pm 13}{-6}=\frac{8}{-6},\frac{-18}{-6}=-\frac{4}{3},3$
So, $-\frac{4}{3}$and 3 are two roots of the given equation.