CBSE Class 9 Answered
If
f(x) = x4 - 2x3 + 3x2 - ax + b is divided
by(x - 1) and (x + 1), it leaves the remainder 5 and 19 respectively. Find
'a' and 'b'.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Given f(x) = x4 - 2x3 + 3x2 - ax + b
When f(x) is divided by (x-1), it leaves a remainder 5
f(1) = 5
1 - 2(1)3 + 3(1)2 - a(1) + b = 5
1 - 2 + 3 - a +b = 5
-a + b = 3 … (i)
When f(x) is divided by (x+1), it leaves a remainder 19
f(-1) = 19
(-1)4 - 2(-1)3 + 3(-1)2 - a(-1) + b = 19
1 + 2 + 3 + a + b = 19
a +b = 13 … (ii)
Adding (i) and (ii),
2b = 16 b = 8
(i) a = b - 3 = 8 - 3 = 5
Answered by | 04 Jun, 2014, 03:23: PM
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