Question

Find the value of a , if x - a is a factor of x^3 - 2ax^2 + x - a + 1 ?

Answer 1

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

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