Question

Find the the roots of $-3x^2+5x+12=0$ by using the quadratic formula.

• A. -$\frac{5}{3},3$
• B. $\frac{5}{3},3$
• C. $\frac{4}{3},3$
• D. -$\frac{4}{3},3$

Answer 1

The correct option is D -$\frac{4}{3},3$

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,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$=\frac{-\left(5\right)\pm \sqrt{(5{)}^2-4(-3\left)\right(12)}}{2(-3)}=\frac{-5\pm \sqrt{25+144}}{-6}=\frac{-5\pm \sqrt{169}}{-6}=\frac{-5\pm 13}{-6}\Rightarrow x=\frac{8}{-6},x=\frac{-18}{-6}\Rightarrow x=-\frac{4}{3},3$

So, $-\frac{4}{3}$ and 3 are the two roots of the given equation.