Question

find the value of a if x-a is a factor of x3-ax2+2x+a-1

Answer 1

Hi there !!!

Given,

x - a is a factor of
${x}^{3} - ax {}^{2} + 2x + a - 1$
we know,
x - a = 0
x = 0+a = a

Substitung the value of x as a,
we have,

(a)^3 - a(a)^2 + 2(a) + a - 1 =0

a^3 - a^3 + 2a + a - 1=0

3a - 1=0

3a =1

a = 1/3

Thus
a = 1/3

Answer 2

Answer:

$x-a$ is a factor of $p(x)=x^{3}-ax^{2}+2x+a-1$ if $a=\frac{1}{3}$

Step-by-step explanation:

Let $p(x)=x^{3}-ax^{2}+2x+a-1$ be the polynomial.

$x-a$ is a factor of $p(x)=x^{3}-ax^{2}+2x+a-1$ then $x=a$ must satisfy $p(x)=0$

i.e., $p(a)=0$

So, $p(a)=a^{3}-aa^{2}+2a+a-1=0$

$\Rightarrow a^{3}-a^{3}+3a-1=0$

$\Rightarrow 3a-1=0$

$\Rightarrow a=\frac{1}{3}$