Question

Determine the value of 'a' if (x-a) is a factor of the polynomial x^3-(a^2-1)x+2.

Answer 1

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Answer 2

Answer:

If [x-a] is a factor of x³-[a²-1] x+2 , then:

f [x] = x³-[a²-1] x+2  [Note: the term: [a²-1] is only multiplied by x and not 2, you may be confused because both are together]

then, f [a] = a³- [a²-1] a+2=0, As x+a =0 nad x=a;

Then f [a] = a³-a³+a+2

⇒ a³-a³=0

Then;

a+2 = 0,

Then a = -2.

Expert Verified Answer* by Venkatarajesh75