The 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 Discriminant value of 0 indicate?

Back

A Discriminant value of 0 indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a positive Discriminant value indicate?

Back

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

Front

What does a negative Discriminant value indicate?

Back

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

Front

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

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0.

Front

Calculate the Discriminant for the quadratic equation: 2x² + 3x - 5.

Back

D = (3)² - 4(2)(-5) = 9 + 40 = 49.

Front

Calculate the Discriminant for the quadratic equation: x² + 2x + 5.

Back

D = (2)² - 4(1)(5) = 4 - 20 = -16.

Front

Calculate the Discriminant for the quadratic equation: 3x² - 6x + 3.

Back

D = (-6)² - 4(3)(3) = 36 - 36 = 0.

Front

What is the significance of the Discriminant in graphing a quadratic function?

Back

The Discriminant helps determine the number and type of x-intercepts of the quadratic function's graph.

Front

If the Discriminant is 49, how many real roots does the quadratic equation have?

Back

The quadratic equation has two distinct real roots.