The discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula ax² + bx + c = 0.

Front

What does a positive discriminant indicate about the solutions of a quadratic equation?

Back

A positive discriminant indicates that there are two distinct real solutions.

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates that there are no real solutions, only complex solutions.

Front

What does a zero discriminant indicate about the solutions of a quadratic equation?

Back

A zero discriminant indicates that there is exactly one real solution, also known as a repeated or double root.

Front

How do you calculate the discriminant for the quadratic equation 3x² + 2x - 1 = 0?

Back

The discriminant is calculated as b² - 4ac = (2)² - 4(3)(-1) = 4 + 12 = 16.

Front

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

Back

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

Front

What is the significance of the discriminant in determining the nature of the roots of a quadratic equation?

Back

The discriminant helps determine whether the roots are real and distinct, real and equal, or complex.

Front

For the quadratic equation x² - 6x + 9 = 0, what is the value of the discriminant?

Back

The discriminant is 0, indicating one real solution.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is D = b² - 4ac.

Front

If a quadratic equation has a discriminant of 25, how many real solutions does it have?

Back

It has two distinct real solutions.