Find the values of a and b if the remainder is 20, when 4 + 9 3 + 8 2 + + is divided by 2 + 5
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Answer:Let us first divide the given polynomial x
4
+x
3
+8x
2
+ax+b by (x
2
+1) as shown in the above image:
From the division, we observe that the quotient is x
2
+x+7 and the remainder is (a−1)x+(b−7).
Since it is given that x
4
+x
3
+8x
2
+ax+b is exactly divisible by x
2
+1, therefore, the remainder must be equal to 0 that is:
(a−1)x+(b−7)=0
⇒(a−1)x+(b−7)=0⋅x+0
⇒(a−1)=0,(b−7)=0(By comparing coefficients)
⇒a=1,b=7
Hence, a=1 and b=7.
Step-by-step explanation:
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