Question

Which of the following best represents the roots of the quadratic function shown?

A. Two real and distinct roots
B. One real root
C. Two complex roots
D. No real roots

Answer 1

The discriminant determines the type of roots a quadratic function has. If the discriminant is greater than 0, there are two real and distinct roots. If it is equal to 0, there is one real root. If it is less than 0, there are two complex roots. If it is less than 0, there are no real roots.

Step-by-step explanation:

The roots of a quadratic function can be determined based on the discriminant, which is b^2 - 4ac in the quadratic equation ax^2 + bx + c = 0. If the discriminant is greater than 0, the quadratic function has two real and distinct roots. If the discriminant is equal to 0, the quadratic function has one real root. If the discriminant is less than 0, the quadratic function has two complex roots. If the quadratic function has no real roots, then the discriminant is less than 0.

For example, if the discriminant is 4, the quadratic function has two real and distinct roots. If the discriminant is 0, the quadratic function has one real root. If the discriminant is -4, the quadratic function has two complex roots. If the discriminant is less than -4, the quadratic function has no real roots.