Question

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

x² + x + 2 = 0

Answer 1

We have been given, x² + x + 2 = 0

Now we also know that for an equation ax² + bx + c = 0, the discriminant is given by the following equation:

D = b² - 4ac

Now, according to the equation given to us, we have,a = 1, b = 1 and c = 2.

Therefore, the discriminant is given as,

D = (1)² - 4(1)(2)

= 1 - 8

= -7

Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation does not satisfies this condition, hence it does not have real roots.