Quadratic Formula and Discriminant

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. It indicates whether the roots are real or imaginary.

Front

If the discriminant is positive, how many real solutions does the quadratic equation have?

Back

Two real solutions.

Front

If the discriminant is zero, how many real solutions does the quadratic equation have?

Back

One real solution.

Front

If the discriminant is negative, how many real solutions does the quadratic equation have?

Back

No real solutions (two imaginary solutions).

Front

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

Back

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

Front

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

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0 (zero, one real solution).

Front

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

Back

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

Front

What is the significance of a positive discriminant?

Back

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

Front

What is the significance of a zero discriminant?

Back

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