Question

Find a polynomial function of degree 4 with - 3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.

Answer 1

Answer:

$f(x) = x^4 + 9x^3 + 27x^2 + 27x$

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.

- 3 as a zero of multiplicity 3

So

$f(x) = (x - (-3))^3 = (x + 3)^3 = x^3 + 9x^2 + 27x + 27$

0 as a zero of multiplicity 1.

So

$f(x) = x(x^3 + 9x^2 + 27x + 27) = x^4 + 9x^3 + 27x^2 + 27x$

(Use 1 for the leading coefficient.)

Multiply the polynomial by 1, so it stays the same. The polynomial in expanded form is:

$f(x) = x^4 + 9x^3 + 27x^2 + 27x$