Question

Write the quadratic equation whose roots are 2 and −6, and whose leading coefficient is 4.

Answer 1

4x^2 + 16x - 48

Explanation:

A quadratic equation with roots 2 and -6 has to have factors of (x - 2) and (x + 6) since both equal 0 when either 2 or 6 are plugged in. To get a leading coefficient of 4, multiply the product of the two factors by 4. When the 4 is distributed it becomes the leading coefficient:

4(x - 2)(x + 6)

4(x^2 + 4x - 12)

4x^2 + 16x - 48