Solve by Factoring:.

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Presentation transcript:

Solve by Factoring:

Solve by completing the Square:

Complex Numbers: Consists of a real number plus an imaginary number Looks like: a + bi Can also be called an imaginary number If a = 0, then it’s a pure imaginary number

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Rational Root Test

Objective Use the Rational Root Theorem

Objective Learn how to evaluate data from real world applications that fit into a quadratic model.

Remainder Theorem Remainder = f(k) Example: f(2)=

Therefore, x = -2 is NOT a root! Find the remainder: Therefore, x = -2 is NOT a root! Factor Theorem

Factor Theorem f(x) has a factor (x-k) iff f(k)=0.

Rational Root Theorem If f(x)=anxn + an-1xn-1 +… + a1x + a0 Then the possible rational roots are Factors of the last term (a0) over the factors of the first term (an)

Example

Find all real roots: x y 1 Mult. of 2 Touches. Goes Through

Find all real roots:

Find all real roots: x y 3 Goes Through ALL

Find all real roots: x y All Go Through -6

Find all real roots:

Find all real roots: Do NOT Graph. NOT Real!

Find all real roots: Do NOT Graph.

Find all real roots:

Find all real roots:

Complex Numbers

Imaginary Unit (i) =