Solving Quadratic Equations (All Methods + Complex Solutions)

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of 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, using the quadratic formula, and graphing.

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.

Front

What does the discriminant tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means two complex roots.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac and add to b, then rewrite the equation as (px + q)(rx + s) = 0.

Front

What are complex solutions?

Back

Complex solutions are solutions to equations that include imaginary numbers, typically in the form a + bi, where i is the imaginary unit.

Front

Solve for x: x² + 4x + 4 = 0

Back

x = -2 (double root).

Front

Solve for x: 2x² - 8 = 0

Back

x = 2, -2.

Front

Solve for x: x² - 6x + 10 = 0

Back

x = 3 + i, 3 - i.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into the form (x - p)² = q, making it easier to solve.