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, given by the formula b² - 4ac.

Front

What does a positive discriminant indicate about the x-intercepts of a quadratic function?

Back

A positive discriminant indicates that the quadratic function has 2 distinct real x-intercepts.

Front

What does a zero discriminant indicate about the x-intercepts of a quadratic function?

Back

A zero discriminant indicates that the quadratic function has exactly 1 real x-intercept (a repeated root).

Front

What does a negative discriminant indicate about the x-intercepts of a quadratic function?

Back

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

Front

Calculate the discriminant for the quadratic equation: 3x² + 6x + 2 = 0.

Back

The discriminant is 6² - 4(3)(2) = 36 - 24 = 12 (positive, so 2 x-intercepts).

Front

Calculate the discriminant for the quadratic equation: x² - 4x + 4 = 0.

Back

The discriminant is (-4)² - 4(1)(4) = 16 - 16 = 0 (one x-intercept).

Front

Calculate the discriminant for the quadratic equation: 2x² + 3x + 5 = 0.

Back

The discriminant is 3² - 4(2)(5) = 9 - 40 = -31 (negative, no real x-intercepts).

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

If a quadratic function has a discriminant of 25, how many x-intercepts does it have?

Back

It has 2 x-intercepts.

Front

If a quadratic function has a discriminant of -16, how many x-intercepts does it have?

Back

It has 0 x-intercepts.