Discriminant of Quadratic Equations

Front

What is the discriminant of 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 helps determine the nature of the roots.

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 solutions.

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 solutions, but two complex (imaginary) solutions.

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 solution, also known as a repeated or double root.

Front

Given the quadratic equation y = x² + 4x + 4, what is the discriminant?

Back

The discriminant is 0, calculated as D = 4² - 4(1)(4) = 16 - 16 = 0.

Front

Identify the values of a, b, and c in the equation 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

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

Back

The quadratic function has two x-intercepts.

Front

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

Back

The quadratic function has one x-intercept.

Front

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

Back

The quadratic function has no x-intercepts.

Front

What is the formula for calculating the discriminant?

Back

D = b² - 4ac.