Discriminant

Front

What is the Discriminant in a quadratic equation?

Back

The Discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by the formula D = b² - 4ac.

Front

What does a positive Discriminant indicate about the roots of a quadratic equation?

Back

A positive Discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a Discriminant of zero indicate about the roots of a quadratic equation?

Back

A Discriminant of zero indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative Discriminant indicate about the roots of a quadratic equation?

Back

A negative Discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

Calculate the Discriminant for the quadratic equation: 2x² + 4x + 2.

Back

D = b² - 4ac = 4² - 4(2)(2) = 16 - 16 = 0.

Front

Calculate the Discriminant for the quadratic equation: x² - 5x + 6.

Back

D = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1.

Front

Calculate the Discriminant for the quadratic equation: 3x² + 2x + 1.

Back

D = b² - 4ac = 2² - 4(3)(1) = 4 - 12 = -8.

Front

If the Discriminant is 36, how many real roots does the quadratic equation have?

Back

The quadratic equation has two distinct real roots.

Front

If the Discriminant is -124, how many real roots does the quadratic equation have?

Back

The quadratic equation has no real roots.

Front

If the Discriminant is 256, how many real roots does the quadratic equation have?

Back

The quadratic equation has two distinct real roots.