Find the roots of the polynomial function f(x) = x3 + 2x2 + x x = 0, x = –1 x = 0, x = 1 with multiplicity 2 x = 0, x = –1 with multiplicity 2

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travispearson43 travispearson43 · Answer 1 · 2018-09-20T22:05:58+02:00

f(x) = -3x2(x - 3)(x + 4)3(x2 + 5)

If (x - a) if a factor of polynomial P(x), then a is a zero of P(x).

x = 0

x = 3

x = -4, three times

x = ±√5

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shristiparmar1221 shristiparmar1221 · Answer 2 · 2021-12-01T14:47:04+01:00

x=0 is a multiplicity of 1 and x=-1 is a multiplicity of 2.

Therefore, option (c) is correct.

Given : The polynomial function [tex]x^{3}+2x^{2} +x[/tex].

We need to determined the roots of the polynomial function [tex]x^{3}+2x^{2} +x[/tex].

For further solution,

[tex]\begin{aligned}x^{3}+2x^{2} +x&=x(x^2+2x+1)\\&=x(x+1)^2\end{aligned}[/tex]

Now, for finding the roots of the above expression, we need to equate the whole expression with 0.

[tex]x(x+1)^2=0\\x=0,-1,-1[/tex]

Hence ,x=0 is a multiplicity of 1 and x=-1 is a multiplicity of 2.

Therefore, option (c) is correct.

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