Solving Quadratic Equations

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 does it mean to solve a quadratic equation by taking the square root?

Back

It means to isolate the variable on one side of the equation and then apply the square root to both sides, considering both the positive and negative roots.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x + a)² = x² + 2ax + a².

Front

Solve by taking the square root: (x - 2)² = 49

Back

x = 9 or x = -5

Front

Solve the quadratic equation: x² + 9x + 20 = 0

Back

x = -5 and x = -4

Front

Find the missing value 'c' to create a perfect square trinomial: x² + 10x + ___

Back

c = 25

Front

Solve by taking the square root: x² = 25

Back

x = ±5

Front

Solve by taking the square root: -5x² = -50

Back

x = ±√10

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

What is the discriminant in a quadratic equation?

Back

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