Question

Find ihe value of a , if x-a is a factor of x3-ax2+2x+a-1

Answer 1

The value of a is 1/3

Given :-

♦ (x-a) is a factor of x³-ax²+2x+a-1

To find :-

♦ The value of ' a '

Solution :-

Given Cubic polynomial is P(x) = x³-ax²+2x+a-1

Given factor of P(x) = (x-a)

We know that,

By Factor Theorem

If (x-a) is a factor of P(x) then P(a) = 0

=> P(a) = 0

=> (a)³-a(a)²+2(a)+a-1 = 0

=> a³-a³+2a+a-1 = 0

=> (a³-a³)+(2a+a)-1 = 0

=> 0 + 3a - 1 = 0

=> 3a - 1 = 0

=> 3a = 1

=> a = 1/3

Therefore, a = 1/3

Answer :-

♦ The value of a is 1/3

Used Theorem :-

Factor Theorem :-

" Let P(x) be a polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial, if (x-a) is a factor of P(x) then

P(a) = 0 , vice-versa.