Question

10. Write a polynomial in factored form with a single root at 0 and a double

Answer 1

Answer:

One possible polynomial is given by: $f(x) = -x(x-3)^2$

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ such that it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$, in which a is the leading coefficient.

Single root at 0, double root at 3:

This means that:

$f(x) = a(x - 0)(x - 3)(x - 3) = ax(x-3)^2$

Decreases as x approaches infinity.

This means that the leading coefficient should be negative. I am going to use -1. So

$f(x) = -x(x-3)^2$