Question

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

Answer 1

Answer:

⇒  (x−a) is factor of x3−ax2+2x+a−1

⇒  Then, a is the zero of polynomial p(x)=x3−ax2+2x+a−1

⇒  p(x)=x3−ax2+2x+a−1

⇒  p(a)=(a)3−a(a)2+2(a)+a−1

⇒  0=a3−a3+2a+a−1

⇒  a3−a3+2a+a−1=0

⇒  3a−1=0

⇒  3a=1

∴   a=1/3

Answer 2

Answer:

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