How do you form a polynomial function whose zeros, multiplicities and degrees are given: Zeros: -2, 2, 3; degree 3?

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How do you form a polynomial function whose zeros, multiplicities and degrees are given: Zeros: -2, 2, 3; degree 3?

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Answer 1 · 2016-11-15T10:58:39

Polynomial function is $x^{3} - 3 x^{2} - 4 x + 12$ $x^3-3x^2-4x+12$

Explanation:

A polynomial function whose zeros are $α$ $alpha$ , $β$ $beta$ , $γ$ $gamma$ and $δ$ $delta$ and multiplicities are $p$ $p$ , $q$ $q$ , $r$ $r$ and $s$ $s$ respectively is

${(x - α)}^{p} {(x - β)}^{q} {(x - γ)}^{r} {(x - δ)}^{s}$ $(x-alpha)^p(x-beta)^q(x-gamma)^r(x-delta)^s$

It is apparent that the highest degree of such a polynomial would be $p + q + r + s$ $p+q+r+s$ .

As zeros are $- 2$ $-2$ , $2$ $2$ and $3$ $3$ and degree is $3$ $3$ , it is obvious that multiplicity of each zero is just $1$ $1$ .

Hence polynomial is $(x - (- 2)) (x - 2) (x - 3)$ $(x-(-2))(x-2)(x-3)$

= $(x + 2) (x - 2) (x - 3)$ $(x+2)(x-2)(x-3)$

= $(x^{2} - 4) (x - 3)$ $(x^2-4)(x-3)$

= $x^{3} - 3 x^{2} - 4 x + 12$ $x^3-3x^2-4x+12$

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How do you form a polynomial function whose zeros, multiplicities and degrees are given: Zeros: -2, 2, 3; degree 3?

1 Answer

Explanation:

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