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A 5th degree polynomial with a root of multiplicity 2 at x = 1, and a root of multiplicity 3 at x = -4, can be written as the function y=(x-1)^a(x-b)^c where​:
a =

b =

c =

The y-intercept of this polynomial is (0, ).


NOTE: Your answers should be integers.

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MrRoyal

Polynomials are expressions represented with variables and constants

The values of a, b and c are:

[tex]a = 2[/tex]

[tex]b = -4[/tex]

[tex]c =3[/tex]

How to determine the missing values

The function is given as:

[tex]y = (x -1)^a(x -b)^c[/tex]

The polynomial has a multiplicity 2 at x = 1.

So, we have:

[tex]y = (x -1)^2(x -b)^c[/tex]

The above means that:

[tex]a = 2[/tex]

The function is a 5th degree polynomial.

This means that:

[tex]a + c = 5[/tex]

Make c the subject

[tex]c = 5 -a[/tex]

Substitute 2 for a

[tex]c = 5 -2[/tex]

[tex]c = 3[/tex]

The polynomial has a multiplicity 3 at x = -4.

So, we have:

[tex]y = (x -1)^2(x + 4)^3[/tex]

The above means that:

[tex]b =-4[/tex]

Hence, the values of a, b and c are:

[tex]a = 2[/tex]

[tex]b = -4[/tex]

[tex]c =3[/tex]

Read more about polynomials at:

https://brainly.com/question/4142886

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