Discriminant Practice

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (D) represent in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

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

Back

D = b² - 4ac = 6² - 4(3)(2) = 36 - 24 = 12.

Front

If the discriminant is negative, what can be said about the solutions of the quadratic equation?

Back

If the discriminant is negative, the quadratic equation has no real solutions; instead, it has two complex solutions.

Front

What is the value of the discriminant for the equation 5x² - 4x + 1 = 0?

Back

D = (-4)² - 4(5)(1) = 16 - 20 = -4.

Front

How many real solutions does a quadratic equation have if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution.

Front

What is the significance of a positive discriminant?

Back

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

Front

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

Back

D = 4² - 4(-1)(-4) = 16 - 16 = 0.

Front

What does it mean if the discriminant is equal to 4?

Back

If the discriminant is equal to 4, the quadratic equation has two distinct real solutions.

Front

For the equation 2x² + 3x + 1 = 0, what is the discriminant?

Back

D = 3² - 4(2)(1) = 9 - 8 = 1.