Discriminant

Front

What is the formula for the discriminant of a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac.

Front

How do you find the zeros of a quadratic equation in factored form?

Back

Set each factor equal to zero and solve for x.

Front

What are the zeros of the equation (x+10)(x-2) = 0?

Back

The zeros are -10 and 2.

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 (the roots are complex).

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 (a repeated root).

Front

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

Back

The discriminant is 76.

Front

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

Back

The discriminant is -39, which is negative.

Front

For the quadratic function y = x² + 4x + 4, what is the value of the discriminant?

Back

The discriminant is zero.

Front

What is the significance of the discriminant in relation to the graph of a quadratic function?

Back

The discriminant helps determine the number and type of x-intercepts (real roots) of the graph.