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 D = b² - 4ac. It determines the nature of the roots of the equation.

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 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

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

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

Back

D = b² - 4ac = 6² - 4(3)(2) = 36 - 24 = 12 (positive discriminant).

Front

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

Back

D = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0 (zero discriminant).

Front

Calculate the discriminant for the equation: 2x² + 4x + 5.

Back

D = b² - 4ac = 4² - 4(2)(5) = 16 - 40 = -24 (negative discriminant).

Front

If the discriminant of a quadratic equation is -3, how many x-intercepts does it have?

Back

0 x-intercepts.

Front

If the discriminant of a quadratic equation is 36, how many x-intercepts does it have?

Back

2 x-intercepts.

Front

What is the formula for calculating the discriminant?

Back

D = b² - 4ac.