Th11.19 Solving using the Quadratic Formula

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 is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the equation.

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 zero discriminant indicate?

Back

A zero discriminant 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 (imaginary) solutions.

Front

Identify a, b, c in the equation: 3x² + 6x + 2 = 0.

Back

a = 3, b = 6, c = 2.

Front

Identify a, b, c in the equation: x² - 4x + 4 = 0.

Back

a = 1, b = -4, c = 4.

Front

Identify a, b, c in the equation: 5x² + 2 = 0.

Back

a = 5, b = 0, c = 2.

Front

Identify a, b, c in the equation: -2x² + 3x - 1 = 0.

Back

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

Front

How do you find the number of solutions using the discriminant?

Back

Calculate the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.