Question

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

Answer 1

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.