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.

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

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!!!

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.

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

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.

Example Find the quadratic equation whose roots are: Find sum and product Find a, b, and c Write equation

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

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