Q. 53.8( 61 Votes )

If f(x) = x4 – 2x2 + ax + b is divided by (x – 2), the remainder is 4. If (a + b) = –4. Find the value of a.

Answer :

Concept Used:


Remainder theorem: If a polynomial f(x) is divided by (x – a) then f(a) will give the remainder.


Explanation:


f(x) = x4 – 2x2 + ax + b


f(2) = (2)4 – 2(2)2 + a.2 + b


f(2) = 16 – 8 + 2a + b


f(2) = 8 + 2a + b


f(2) = 4


8 + 2a + b = 4


2a + b = –4


a + (a + b) = –4


a – 4 = –4


a = 0


Hence, the value of a is 0.

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