Question

Find a polynomial of degree 3 that has zeros 1, -1 and 3 and in which the coefficient of 2 x is 6.

Answer 1

well a polynomial of degree 2 with zeros at 1 and -1 is (x-1)(x+1)

Answer 2

so?

Answer 3

coefficient of 2 x is 6?

Answer 4

In general, a polynomial with roots \(r_1, r_2, ... r_n\) can be written as \[P(x) = k(x-r_1)(x-r_2)...(x-r_n)\] where \(k\) is a constant which does not affect the roots, only the amplitude of the curve. Use this to construct the polynomial with the given roots, and choose \(k\) to get the right coefficient.