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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSN.CN.A.3

Front

Solve for x: x² + 4x + 4 = 0

Back

x = -2 (double root).

Tags

CCSS.HSA-REI.B.4B

Front

Solve for x: 2x² - 8 = 0

Back

x = 2, -2.

Tags

CCSS.8.EE.A.2

Front

Solve for x: x² - 6x + 10 = 0

Back

x = 3 + i, 3 - i.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

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.

Tags

CCSS.HSA-REI.B.4B