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Question

If f(x)=(x−2)(x2−x−a),g(x)=(x+2)(x2+x−b) and their HCF is x2−4, then find a−b (a and b are constants)

A
0
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B
4
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C
1
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D
6
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Solution

The correct option is C 0
Given, f(x)=(x2)(x2xa)
and g(x)=(x+2)(x2+xb)
HCF of f(x) & g(x) is x24=(x2)(x+2)
i.e., bothf(x) & g(x) are divisible by (x2)(x+2)
It means (x2xa) is divisible by x+2
(x2xa)=(x+2)(x3)+(a+6)
Remainder =0
Therefore, a+6=0a=6
Similarly, (x2+xb) is divisible by (x2)
(x2+xb)=(x2)(x+3)+(b+6)
remainder=0
Therefore, b+6=0b=6
ab=66=0

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