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?

Back

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

Front

What does a discriminant of zero indicate?

Back

A discriminant of zero 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

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

Back

D = b² - 4ac = 6² - 4(3)(2) = 36 - 24 = 12 (positive, two real solutions).

Front

Calculate the discriminant for the equation x² - 4x + 4 = 0.

Back

D = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0 (one real solution).

Front

Calculate the discriminant for the equation 2x² + 4x + 5 = 0.

Back

D = b² - 4ac = 4² - 4(2)(5) = 16 - 40 = -24 (negative, no real solutions).

Front

What are the coefficients in the equation y = 2x² + 3x + 1?

Back

a = 2, b = 3, c = 1.

Front

If the discriminant is 9, what can you conclude about the solutions?

Back

There are two distinct real solutions.

Front

If the discriminant is -16, what can you conclude about the solutions?

Back

There are no real solutions, only complex solutions.