Solving Quadratics with Any Method

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, and using the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

What does the discriminant tell you?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

Solve: x² + 2x - 24 = 0

Back

x = -6, x = 4

Front

Solve: x² - 6x + 9 = 0

Back

x = 3, 3

Front

Solve using the quadratic formula: 2x² + 17x + 21 = 0

Back

x = -7, -3/2

Front

Solve using the quadratic formula: x² + 6x - 4 = 36

Back

x = 4, -10

Front

Solve using the quadratic formula: 2n² + 4n - 16 = 0

Back

n = -4, 2