Quadratic Formula & the Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the Discriminant tell us?

Back

The Discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots (the roots are complex).

Front

If the Discriminant is zero, what can we conclude about the roots?

Back

If the Discriminant is zero, the quadratic equation has exactly one real root, which is a repeated root.

Front

Solve the quadratic equation: x² - 4x + 4 = 0

Back

x = 2 (a repeated root).

Front

What is the value of the Discriminant for the equation 3x² + 6x + 3 = 0?

Back

D = 6² - 4(3)(3) = 36 - 36 = 0.

Front

Solve the quadratic equation: 2x² - 8 = 0

Back

x = 2, -2.

Front

What is the significance of a positive Discriminant?

Back

A positive Discriminant indicates that the quadratic equation has two distinct real roots.

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 and a ≠ 0.

Front

Solve the quadratic equation: x² + 5x + 6 = 0

Back

x = -2, -3.

Front

What does it mean if the Discriminant is negative?

Back

If the Discriminant is negative, the quadratic equation has no real roots; the roots are complex.