Math polynomial

Question

Write a quadratic polynomial with roots 9 and -3

write your answer using the variable x and in standard form with a leading coefficient of 1

Answer 1

If the roots are x = 9 and x = -3, then the factors are (x - 9) and (x + 3). That means we can multiply these factors together to get a polynomial that has those roots.

f(x) = (x - 9)(x + 3)

f(x) = x² + 3x - 9x - 27

f(x) = x² - 6x - 27

Note that there are lots of polynomials that have those roots. I could multiply by another factor, such as 2, or 3, or any number or I could multiply by another binomial like (x - 6) and those polynomials will still have 9 and -3 as roots.