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Write the polynomial function, in standard form, that has zeros -3, 4, and 1.

Write the polynomial function, in standard form, that has zeros -3, 4, and 1.-example-1
User Xynariz
by
6.4k points

1 Answer

1 vote

Answer:

OPTION D

Explanation:

Given the zeroes (roots) of a polynomial are: - 3, 4 & 1.

An
$ n -degree $ polynomial has
$ n - roots $ (zeroes). The converse is also true.

Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.

Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.

Here, -3, 4 & 1 are roots. So, the factors are: (x + 3), (x - 4) and (x - 1) .

Multiplying them will result in the polynomial.


$ (x + 3)(x - 4)(x - 1) $


$ \implies (x^2 - 4x + 3x - 12)(x - 1) $


$ \implies x^3 -x^2 - 4x^2 + 4x + 3x^2 - 3x - 12x + 12 $

Simplifying, we get:
$ \textbf{x}^\textbf{3} \textbf{-} \textbf{2x}^\textbf{2} \textbf{-} \textbf{11x} \textbf{+} \textbf{12}$

Hence, OPTION D is the right answer.

User Chris Xue
by
5.9k points
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