Q. 53.8( 70 Votes )

# If f(x) = x^{4} – 2x^{2} + 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) = x^{4} – 2x^{2} + 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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is divided by (x-a)

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