Question

Find the value of a for which (x-1) is a factor of polynomial a2x3-4ax+4a-1.

Answer 1

Solution of this question is that a=1/3

Answer 2

the value of a is 1/3

Correct question

Find the value of a for which (x-1) is a factor of polynomial 3ax^2-4ax+4a-1.

Given

• (x-1) is a factor
• 3ax^2-4ax+4a-1

To find

• the value of a

Solution

we are provided with a polynomial and a factor of it and are asked to find the value of a for which the given condition holds correct.

if x - 1 is a factor of the given polynomial it must satisfy,

p(1) = 0

using this known condition we can estimate the value of a for which the situation will hold.

x - 1 is a factor (given)

x - 1 = 0

or, x = 1

ie, p(1) = 0

or, p(x) = 3ax^2-4ax+4a-1

or, p(1) = 3a (1)^2 - 4a(1) + 4a -1

or, p(1) = 3a - 4a +4a -1

or, p(1) = 3a - 1

from our known condition,

p(1) = 0

or, 3a - 1 = 0

or, 3a = 1

or, a = 1/3

therefore, the value of a is 1/3