Root to factor form

Question

I have another problem that I can’t figure out. It’s the root of 0 with multiplicty of 1 and a root of 3.72 with multiplicty of 1. The y intercept of 0. I tried myself and got 2x^2(x-3.72) but it says it is not right.

Answer 1

You have two roots, each with a multiplicity of one, meaning the root occurs just once. With two roots, the degree of the polynomial is two, meaning the highest exponent is 2 (x²). In factored form:

y = a·(x-0)(x - 3.72) = a·x(x - 3.72) = ax² - 3.72ax

The factor a is the leading coefficient. There isn't enough information in your problem statement to determine its value. You put it down as 2 in your solution, but I can't tell where you got that value from. You also put down an x² term in your factored form which would occur if the zero root had a multiplicity of 2.