Answer:
OPTION D
Step-by-step explanation:
Given the zeroes (roots) of a polynomial are: - 3, 4 & 1.
An [tex]$ n -degree $[/tex] polynomial has [tex]$ n - roots $[/tex] (zeroes). The converse is also true.
Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.
Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.
Here, -3, 4 & 1 are roots. So, the factors are: (x + 3), (x - 4) and (x - 1) .
Multiplying them will result in the polynomial.
[tex]$ (x + 3)(x - 4)(x - 1) $[/tex]
[tex]$ \implies (x^2 - 4x + 3x - 12)(x - 1) $[/tex]
[tex]$ \implies x^3 -x^2 - 4x^2 + 4x + 3x^2 - 3x - 12x + 12 $[/tex]
Simplifying, we get: [tex]$ \textbf{x}^\textbf{3} \textbf{-} \textbf{2x}^\textbf{2} \textbf{-} \textbf{11x} \textbf{+} \textbf{12}$[/tex]
Hence, OPTION D is the right answer.
