Module 3 Final Review

x = 4 and x = 5

8

$$x = -8 \ x = -8 \pm \sqrt{5}$$

$$a = 3 \pm 2\sqrt{3}$$

x = -6 and x = -1

A polynomial equation of the form $$ax^2 + bx + c = 0$$ where a, b, and c are constants and a ≠ 0.

The quadratic formula is $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ used to find the roots of a quadratic equation.

Completing the square is a method used to solve quadratic equations by rewriting them in the form $$(x - p)^2 = q$$ .

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots of the equation.

Imaginary numbers are numbers that can be written as $$bi$$ where $$b$$ is a real number and $$i$$ is the imaginary unit, defined as $$i = \sqrt{-1}$$ .