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Roots of Quadratic Equation

Roots of quad...

Question

Roots of quadratic equation $3 q^{2} = 2 q + 8$ are

q = - 2, \frac{4}{3}

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q = 2, \frac{- 4}{3}

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q = - 2, \frac{- 4}{3}

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q = 2, \frac{4}{3}

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Solution

The correct option is A $q = 2, \frac{- 4}{3}$
Given equation is,
$3 q^{2} = 2 q + 8$
$3 q^{2} - 2 q - 8 = 0$
$3 q^{2} - 6 q + 4 q - 8 = 0$
$3 q (q - 2) + 4 (q - 2) = 8$
$(3 q + 4) (q - 2) = 0$
$∴ q = 2, \frac{- 4}{3}$
$∴$ roots of the given equation are $2, \frac{- 4}{3}$

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