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 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; if D < 0, there are two complex roots.

Front

Solve for x: x² - 4x + 4 = 0

Back

x = 2 (a double root).

Front

What is the value of the discriminant for the equation 2x² + 3x + 1 = 0?

Back

D = 3² - 4(2)(1) = 9 - 8 = 1.

Front

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

Back

There is exactly one real solution (a repeated root).

Front

Solve for x: 2x² + 8x + 6 = 0

Back

x = -3 ± √3.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What happens if the discriminant is negative?

Back

The quadratic equation has two complex (imaginary) solutions.

Front

Solve for x: x² + 2x + 5 = 0

Back

x = -1 ± 2i.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.