Which of the following describes the roots of the polynomial function K x) - (x+ 2)(x-4)(x+1)3?

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Аноним Аноним · Answer 1 · 2019-05-24T15:51:48+02:00

Answer:

It's the first option.

Step-by-step explanation:

(x + 2)^2 gives a duplicate (multiplicity 2) root. (because (x + 2)^2 = 0 so x = -2 multplicity 2)

(x - 4) gives one root of 4.

(x + 1)^3 gives x = -1 with multiplicity 3.

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kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-05-24T15:58:44+02:00

Answer:

-2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.

Step-by-step explanation:

The given polynomial function is: [tex]f(x)=(x+2)^2(x-4)(x+1)^3[/tex].

To find the roots of this polynomial, we equate each factor to zero.

This implies that;

i. [tex](x+2)^2=0[/tex], [tex]\implies x=-2[/tex], the multiplicity of this root is 2, because the factor repeats twice

ii. [tex]x-4=0[/tex], [tex]\implies x=4[/tex], the multiplicity of this root is 1, because the factor repeats once.

ii. [tex](x+1)^3=0[/tex], [tex]\implies x=-1[/tex], the multiplicity of this root is 3, because the factor repeats three times.