Question

A polynomial function has a root of –6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

Answer 1

Answer:

See explanation

Step-by-step explanation:

If a polynomial function has a root of –6 with multiplicity 3, then it has factor $(x+6)^3$

If a polynomial function has a root of 2 with multiplicity 4, then it has factor $(x-2)^4$

If the function has a negative leading coefficient and is of odd degree, then the simpliest function's expression could be

$f(x)=-(x+6)^3(x-2)^4$

The graph of this function is attached.

Answer 2

A polynomial function can be represented on a graph

The given parameters are:

$\mathbf{Root = -6, Multiplicity = 3}$

$\mathbf{Root = 2, Multiplicity = 4}$

So, the equation is represented as:

$\mathbf{f(x) =a (x - Root)^{Multiplicity}}$

This gives

$\mathbf{f(x) = a(x - (-6))^3(x - 2)^4}$

$\mathbf{f(x) =a (x +6)^3(x - 2)^4}$

The equation has a negative leading coefficient.

This means that, the value of a is less than 0 i.e. a < 0

Assume a = -2, the equation becomes

$\mathbf{f(x) = -2(x +6)^3(x - 2)^4}$

See attachment for the possible graph of the function

Read more about polynomial functions at:

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