In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
x2 + x + 2 = 0
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
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.