10.3 Quadratic Equations from their solutions

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Presentation transcript:

10.3 Quadratic Equations from their solutions

Ex 1) Solve by the Quadratic Formula over the set of complex numbers.

Example 1 cont… 1 3 2 goes into all 3 5 OR separate to a + bi

A Root is a Solution or a Zero Ex 2) Solve: EASY! FACTOR it! Roots: 4, -1 Now, you will be given roots → find equation Work Backwards!

Ex 3) Find the quadratic equation whose roots are 2 & –4 Set each = 0 Multiply together Distribute Answer! OR: “Product-Sum” Method: Same Answer!

You must use Product-sum with Rads or i’s Notice the Rules: OPPOSITE of the Sum goes in as your “b” coefficient The Product goes in as your “c” It’s an Equation so it always = 0

Ex 4) Find the quadratic equation whose roots are 3 + i & 3 – i

Ex 5) T.O.O. Find the quadratic equation whose roots are

Ex 6) Factor in a complex number system Ex 6) Factor in a complex number system. (You CAN’T factor since it has “i”s) Steps: Do Quad. Formula Put in parenthesis (x – r1 )(x – r2 ) Simplify Answer:

Ex 7) Factor in a complex number system Ex 7) Factor in a complex number system. (You CAN’T factor since it has “i”s) Roots are: and Answer:

Homework Pg. 528-530 #1-21 EOO, 25-35 odd, 41-51 odd