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 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 two complex (imaginary) 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 of the equation 6x² − 2x − 3 = 0.

Back

The discriminant is 76.

Front

For the equation 10x² - 6x = 0, what is the value of C?

Back

The value of C is 0.

Front

Calculate the discriminant of the equation -2x² − x − 1 = 0.

Back

The discriminant is -7.

Front

How many solutions does the equation x² + 8x + 16 have?

Back

The equation has 1 solution.

Front

What is the formula for the discriminant?

Back

D = b² - 4ac.

Front

If the discriminant is 29, how many real solutions does the quadratic equation have?

Back

The quadratic equation has 2 distinct real solutions.