4.8 Discriminant and The Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (D) indicate in a quadratic equation?

Back

The discriminant D = b² - 4ac indicates the nature of the roots of the quadratic equation: if D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

Solve the quadratic equation: 2x² + 2x - 12 = 0

Back

x = 2, -3.

Front

If the discriminant is zero, what can be said about the solutions?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

Front

Calculate the discriminant for the equation: 6x² - 2x - 3 = 0

Back

The discriminant is 76.

Front

What is the value of the discriminant for the equation: -2x² - x - 1 = 0?

Back

The discriminant is -7.

Front

What does a positive discriminant tell us about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a negative discriminant tell us about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Front

Solve the quadratic equation: x² - 2x - 8 = 0

Back

x = 4, -2.

Front

What is the first step in using the quadratic formula?

Back

Identify the coefficients a, b, and c from the quadratic equation ax² + bx + c = 0.