Question

Without solving the equation, determine the nature of the roots of x^2 - 2x - 8 = 0.

Two, real unequal roots

Two, real equal roots

No real roots

Answer 1

two real, unequal roots

Explanation:

This is a quadratic equation. The quadratic formula can be used to determine how many and what kind of roots may exist:

Find the discriminant, which is defined as b^2 - 4ac, if ax^2 + bx + c = 0. In this case, a = 1, b = -2 and c = -8, so that the discriminant value is

(-2)^2 - 4(1)(-8), or 4 + 32 = 36.

Because the discriminant is real and positive, we know for certain that we have two real, unequal roots