Question

Write the quadratic equation whose roots are 6 and -4 , and whose leading coefficient is 5. (Use the letter x to represent the variable.)

Answer 1

The quadratic equation for this would be f(x) = 5x^2 - 10x - 120.

In order to find that, we need to start by taking our x intercept values and setting them equal to zero.

x = 6 ----> subtract 6 from both sides

x - 6 = 0

x = -4 ----> add 4 to both sides

x + 4 = 0

Now that we have both of these zero terms, we can multiply them to get a standard form.

f(x) = (x - 6)(x + 4)

And while this will give us the zeros we need, it will no give us the lead coefficient. So we must multiply by the desired lead coefficient.

f(x) = 5(x - 6)(x + 4)

f(x) = 5(x^2 - 6x + 4x - 24)

f(x) = 5(x^2 - 2x - 24)

f(x) = 5x^2 - 10x - 120