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

$- \frac{4}{3}$

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$\frac{4}{3}$

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-3

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Solution

The correct options are
A
$- \frac{4}{3}$

C
3

Given equation is $- 3 x^{2} + 5 x + 12 = 0$
On comparing with $a x^{2} + b x + c = 0$ , we get
a=-3, b=5 and c=12
By quadratic formula,
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$= \frac{- (5) \pm \sqrt{(5)^{2} - 4 (- 3) (12)}}{2 (- 3)} = \frac{- 5 \pm \sqrt{25 + 144}}{- 6} = \frac{- 5 \pm \sqrt{169}}{- 6} = \frac{- 5 \pm 13}{- 6} = \frac{8}{- 6}, \frac{- 18}{- 6} = - \frac{4}{3}, 3$

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

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