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 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 zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

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 (the roots are complex).

Front

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

Back

The discriminant is 76.

Front

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

Back

The discriminant is 0.

Front

How many real solutions does the equation -2x² − x − 1 = 0 have if the discriminant is -7?

Back

It has no real solutions.

Front

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

Back

It has two distinct real solutions.

Front

What is the formula for calculating the discriminant?

Back

D = b² - 4ac.

Front

If a quadratic equation has a discriminant of 0, what can be said about its graph?

Back

The graph touches the x-axis at one point (the vertex) and does not cross it.