Question 1 (iii)

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

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

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Solution

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

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