Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

$x^{2} + x + 2 = 0$

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Solution

The given equation is $x^{2} + x + 2 = 0$ .

Comparing it with $a x^{2} + b x + c = 0$ , we get

a = 1, b = 1 and c = 2

∴ Discriminant, D = $b^{2} - 4 a c = 1^{2} - 4 \times 1 \times 2 = 1 - 8 = - 7 < 0$

Hence, the given equation has no real roots (or real roots does not exist).

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