Warm Up – Look over your notes/examples from last week Any questions??

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Presentation transcript:

Warm Up – Look over your notes/examples from last week Any questions??

Pop Quiz! – Clear your desk except for a pencil & calculator!

Guided Notes – complete from Friday

6.5 Theorems About Roots

The Degree REMEMBER: the DEGREE of a polynomial is the highest exponent! The Degree also tells us the number of Solutions! Including Real AND Imaginary!

Irrational Root Theorem and Imaginary Root Theorem Irrational Root Theorem Square Root Solutions come in PAIRS! If x2 = c then x = ± √c If √ is a solution so is -√ Imaginary Root Theorem If a + bi is a solution, so is a – bi

Get ready! Solve the following by taking the square root. X2 – 49 = 0 X2 + 36 = 0

Using the Theorems √5 2. 4i 3. 2 – i 4. 2 - √3 Given one Root, find the other root! √5 2. 4i 3. 2 – i 4. 2 - √3

Zeros to Factors If a is a zero, then (x – a) is a factor!!

Examples Find a 2nd degree equation with roots 2 and 3 Find a 2nd degree equation with roots -1 and 6

Examples Find a 2nd degree equation with roots 0 and 4 Find a 2nd degree equation with roots ±√7

Examples Find a 2nd degree equation with roots ±2√5 Find a 2nd degree equation with roots ±6i

Examples Find a 2nd degree equation with roots 2 – 3i and 2 +3i

Find a 2nd degree equation with a root of 7 + i

Examples Find a 3rd degree equation with roots 4 and 3i

Extra Practice – Solving How many solutions will each equation have? Find them! x3 – 6x2 – 16x = 0 X3 + 343 = 0

Solving by Graphing Keep in mind, Solving by Graphing ONLY works for REAL SOLUTIONS. You cannot find Imaginary solutions from a Graph. Roots: This is another word for zeros or solutions.

Example: Solve x3 – 5x2 - 2x + 24 = 0

Example 24x3 – 22x2 - 5x + 6 = 0

Solve x3 – 5x2 + 7x – 35 = 0