If f(1) = 0, what are all the roots of the function mc021-1.jpg? use the remainder theorem.

Asked by maham237 @ 02/12/2020 in Mathematics viewed by 313 People

A. x = –1, x = 1, or x = 3
B. x = –3, x = –1, or x = 1
C. x = –3 or x = 1
D. x = –1 or x = 3

Answered by maham237 @ 02/12/2020

Solution:

As we are given that f(1) = 0 .

It mean that $(x-1)$ is one of the factor of the given equation.

Remainder theorem can be applied as below:

$\frac{(x^3+3x^2-x-3)}{(x-1)}=\frac{x^3-x^2+4x^2-4x+3x-3}{(x-1)}\\ \\\frac{x^3-x^2+4x^2-4x+3x-3}{(x-1)}=\frac{x^2(x-1)+4x(x-1)+3(x-1)}{(x-1)} \\\\\frac{x^2(x-1)+4x(x-1)+3(x-1)}{(x-1)}=\frac{(x^2+4x+3)(x-1)}{(x-1)} \\\\\frac{(x^2+4x+3)(x-1)}{(x-1)} =\frac{(x^2+3x+x+3)(x-1)}{(x-1)} \\\\\frac{(x^2+3x+x+3)(x-1)}{(x-1)} =\frac{(x-1)(x+3)(x+1)}{(x-1)}$

Hence the factors are (x-1),(x+3) and (x+1).

Hence the correct option is B.

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