Question

if (x-a) is factor of x³+2x-ax²+a-1 what is the value of a
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Answer 1

Answer:

⇒ (x−a) is factor of x

3

−ax

2

+2x+a−1

⇒ Then, a is the zero of polynomial p(x)=x

3

−ax

2

+2x+a−1

⇒ p(x)=x

3

−ax

2

+2x+a−1

⇒ p(a)=(a)

3

−a(a)

2

+2(a)+a−1

⇒ 0=a

3

−a

3

+2a+a−1

⇒ a

3

−a

3

+2a+a−1=0

⇒ 3a−1=0

⇒ 3a=1

∴ a=

3

1