Presentation on theme: "Can we determine a quadratic equation if we have its roots?"— Presentation transcript:
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 ExampleWhat are the sum and product of the roots of the equation 3x2-6x+8=0SumProduct
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 productFind a, b, and cWrite equation
8 Try on your ownFind the quadratic equation whose roots are 5+2i and 5-2i.
9 Summary/HWHow can we determine a quadratic equation if we have the roots of the equation?HW pg 87, 1-10