Question

Write the general polynomial p(x) if its only zeros are 1 4 and -3 with multiplicites 3 2 and 1 respectively what is the degree

Answer 1

Answer:

The 6th degree polynomial is $p(x) = (x-1)^3(x-4)^2(x+3)$

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.

Zero 1 with multiplicity 3.

So

$p(x) = (x-1)^3$

Zero 4 with multiplicity 2.

Considering also the zero 1 with multiplicity 3.

$p(x) = (x-1)^3(x-4)^2$

Zero -3 with multiplicity 1:

Considering the previous zeros:

$p(x) = (x-1)^3(x-4)^2(x-(-3)) = (x-1)^3(x-4)^2(x+3)$

Degree is the multiplication of the multiplicities of the zeros. So

3*2*1 = 6

The 6th degree polynomial is $p(x) = (x-1)^3(x-4)^2(x+3)$