1. 10.3 Quadratic Equations from their solutions

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

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

4. 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!

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

6. 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

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

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

9. 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:

10. 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:

11. Homework
Pg #1-21 EOO, odd, odd