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**Can we determine a quadratic equation if we have its roots?**

Do Now: Use the quadratic formula to determine the general form of BOTH roots to any quadratic equation.

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**What is the sum of the roots of a quadratic equation?**

We determined that the general form of the two roots can be written as: To find the sum, we add these together

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**The sum of the roots is always the same?**

Yes, for any quadratic equation, due to the nature of the roots, the sum of the roots is the opposite of b over a. If we know one root and the sum of the roots, we can find the other root. Note: If we know that one root is imaginary, then the other root is the CONJUGATE!!!

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**Is there a similar relationship for the product of the roots?**

Yes! We can use the general form of the roots to find the product.

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Example What are the sum and product of the roots of the equation 3x2-6x+8=0 Sum Product

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**Why do we care about the sum and product of roots?**

If we know the sum and product, we can write the original quadratic equation. The sum is made of b and a, and the product is made of c and a, so we have everything we need to write the quadratic equation.

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**Example Find the quadratic equation whose roots are:**

Find sum and product Find a, b, and c Write equation

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Try on your own Find the quadratic equation whose roots are 5+2i and 5-2i.

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Summary/HW How can we determine a quadratic equation if we have the roots of the equation? HW pg 87, 1-10

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Aim: How do we solve quadratic equation with complex roots? Do Now: 1. Solve for x: 2. Solve for x: 3. Solve for x: HW: p.219 # 6,8,10,12,14 p.241 # 6,14,25.

Aim: How do we solve quadratic equation with complex roots? Do Now: 1. Solve for x: 2. Solve for x: 3. Solve for x: HW: p.219 # 6,8,10,12,14 p.241 # 6,14,25.

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