Presentation is loading. Please wait.

Presentation is loading. Please wait.

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.

Similar presentations


Presentation on theme: "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."— Presentation transcript:

1

2 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.

3 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

4 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!!!

5 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.

6 Example What are the sum and product of the roots of the equation 3x 2 -6x+8=0 Sum Product

7 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.

8 Example Find the quadratic equation whose roots are: 1)Find sum and product 2)Find a, b, and c 3)Write equation

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

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


Download ppt "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."

Similar presentations


Ads by Google