6. The polynomial f(x)= x4
– 2x3
+3x2
– ax + b when divided by (x – 1) and (x + 1) leaves the
remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when
f(x) is divided by (x – 3).
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Answers
Answered by
355
heya folk !!!!
f(x) = x4 - 2x3 + 3x2 - ax + b
f(1)=5 and f(-1)=19 ( from given question )
14 - 2.13 + 3.12 - a.1 + b =5 and (-1)4 - 2(-1)3 + 3(-1)2 - a(-1) + b=19
=> 1-2+3-a+b=5 and 1+2+3+a+b=19
=>2-a+b=5 and 6+a+b=19
=>-a+b=5-2 and a+b=19-6
=>-a+b=3.....(1) and a+b=13....(2)
on subtracting (1) from (2), we get:
a+b-(-a+b)=13-3
a+b+a-b=10
2a=10
a=5
placing a=5 in equation 1, we get,
-5+b=3 , b=8
a=5, b=8
hope this helps u
f(x) = x4 - 2x3 + 3x2 - ax + b
f(1)=5 and f(-1)=19 ( from given question )
14 - 2.13 + 3.12 - a.1 + b =5 and (-1)4 - 2(-1)3 + 3(-1)2 - a(-1) + b=19
=> 1-2+3-a+b=5 and 1+2+3+a+b=19
=>2-a+b=5 and 6+a+b=19
=>-a+b=5-2 and a+b=19-6
=>-a+b=3.....(1) and a+b=13....(2)
on subtracting (1) from (2), we get:
a+b-(-a+b)=13-3
a+b+a-b=10
2a=10
a=5
placing a=5 in equation 1, we get,
-5+b=3 , b=8
a=5, b=8
hope this helps u
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