Question

If the discriminant of a quadratic equation is equal to -8 , which statement describes the roots?

Answer 1

Answer: There are no real number roots (the two roots are complex or imaginary)

The discriminant D = b^2 - 4ac tells us the nature of the roots for any quadratic in the form ax^2+bx+c = 0

There are three cases

• If D < 0, then there are no real number roots and the roots are complex numbers.
• If D = 0, then we have one real number root. The root is repeated twice so it's considered a double root. This root is rational if a,b,c are rational.
• If D > 0, then we get two different real number roots. Each root is rational if D is a perfect square and a,b,c are rational.