For what value of k is (x + 1) a factor of x³ + kx² – x + 2?

(a) 4
(b) 3
(c) 1
(d) -2

Anurag Mishra Professor Asked on 19th February 2016 in Maths.
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1 Answer(s)

Answer: (d) – 2

Solution:-
If (x + 1) a factor of x^3 + kx^2 – x + 2. 
So,  x + 1 = 0 
 x = – 1

Put the value of x = -1, 
Then, (-1)^3 + k (-1)^2 – (-1) + 2 = 0
 = – 1 + k + 1 + 2 = 0 
k + 2 = 0
k = -2

Then, the value of ‘k’ is -2. 

Hence, the correct answer is option (d) -2. 

Anurag Mishra Professor Answered on 19th February 2016.
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