Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac, where a, b, and c are coefficients of the quadratic equation ax² + bx + c.

Front

What does a positive discriminant indicate about the roots of a quadratic function?

Back

A positive discriminant indicates that the quadratic function has two distinct real roots.

Front

What does a zero discriminant indicate about the roots of a quadratic function?

Back

A zero discriminant indicates that the quadratic function has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate about the roots of a quadratic function?

Back

A negative discriminant indicates that the quadratic function has no real roots (the roots are complex).

Front

Calculate the discriminant for the quadratic equation y = 2x² + 3x + 1.

Back

The discriminant is b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1 (positive).

Front

Calculate the discriminant for the quadratic equation y = x² - 4x + 4.

Back

The discriminant is b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0.

Front

Calculate the discriminant for the quadratic equation y = x² + 2x + 5.

Back

The discriminant is b² - 4ac = 2² - 4(1)(5) = 4 - 20 = -16 (negative).

Front

If the discriminant is 0, how many x-intercepts does the quadratic function have?

Back

The quadratic function has exactly 1 x-intercept.

Front

If the discriminant is positive, how many x-intercepts does the quadratic function have?

Back

The quadratic function has 2 x-intercepts.

Front

If the discriminant is negative, how many x-intercepts does the quadratic function have?

Back

The quadratic function has 0 x-intercepts.