Question

Write a quadratic equation with the given roots. Write the equation in the form ax2 + bx + c = 0 where a, b, and c are integers. -10 and -2

Answer 1

A quadratic with roots at 8 and 5 is f(x) = x^2 +12x + 20

In order to find an equation given roots you can create statements that equal 0 in order to create parenthesis. For instance we know x = 8 at one point. So, we can solve that to equal 0.

x = -2 ----> add 2 to both sides

x + 2 = 0

We can do the same for the other zero.

x = -10 ----> add 10 to both sides

x + 10 = 0

Now that we have both of these, we can multiply these two things together. This will give us the function we need.

f(x) = (x + 2)(x + 10)

f(x) = x^2 + 10x + 2x + 20

f(x) = x^2 + 12x + 20