Find the roots of $2 x^{2} + x - 4 = 0$ by quadratic formula.

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Solution

$2 x^{2} + x - 4 = 0$
Compairing with $a x^{2} + b x + c = 0$
a = 2 b = 1 c = -4
$∴ \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$= \frac{- 1 \pm \sqrt{1^{2} - 4 \times 2 (- 4)}}{2 \times 2}$
$\frac{- 1 \pm \sqrt{33}}{4}$
$∴ x = \frac{- 1 + \sqrt{33}}{4}$ OR $x = \frac{- 1 - \sqrt{33}}{4}$

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