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

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:

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

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  1. 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.

  2. 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

  3. 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!!!

  4. 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.

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

  6. 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.

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

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

  9. 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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