Aim: What are the properties of a quadratic equation? Do Now: 1. Solve for x: Sum of the roots = 2 + 3 = 5, product of the roots = 6 x = 2, 3 2. Solve for x: x2 + 7x – 18 = 0 x = -9, 2 Sum of the roots = -7, product of the roots = -18 HW: p.223 # 8,10,14,20,28,32,38 p.243 # 76

#1: The sum of the roots is 5 that equals the opposite coefficient of the x term over the leading coefficient. The product of the roots is 6 that equals the constant over the leading coefficient #2: The sum of the roots is -7 that equals the opposite coefficient of the x term over the leading coefficient. The product of the roots is -18 that equals the constant over the leading coefficient

From the previous examples, we can come up with the formulas: The standard quadratic equation ax2+ bx + c = 0 The sum of the roots of a quadratic equation is equal to The product of the roots is equal to

Find the sum and product of the roots of

We can also use this property to find the quadratic equation. Ex: The roots of a quadratic equation are and Sum of the roots: Product of the roots: so b = –6, so c = 7 Therefore, the equation is

1. Find the sum and the product of the roots of the equation: b) c) d)

2. If and the product of the roots is 20 find the value of k. 3. If x2 + bx – 6 = -9x , and the sum of the root is 35, find the value of b 4. If the roots of a quadratic equation are given, what is the equation? a) x = –2, 4 b) x = c) x =