Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value that determines the nature of the roots of a quadratic equation, given by the formula b² - 4ac.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Front

How do you find the discriminant of the equation -5x² - 6 = 0?

Back

The discriminant is calculated as b² - 4ac. Here, a = -5, b = 0, c = -6, so the discriminant is 0² - 4(-5)(-6) = -120.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

Identify a, b, and c in the equation 8x² + 3x - 6 = 3x.

Back

In standard form, a = 8, b = 0, c = -6.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

How many solutions does the quadratic x² - 6x + 9 = 0 have?

Back

The discriminant is 0, indicating that there is 1 solution.

Front

If the discriminant is -2, how many solutions are there?

Back

If the discriminant is -2, there are no real solutions.