6. Find the value of b so that x4 + x3 + 8x2 + x + b is exactly divisible by x4 +1. Ans.
Answers
Step-by-step explanation:
let's use bodmass theorem alright
x10+8=x18
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Class 10
>>Maths
>>Polynomials
>>Division Algorithm for Polynomials
>>Find the values of a and b so that x^4 +
Question
Bookmark
Find the values of a and b so that x
4
+x
3
+8x
2
+ax+b is divisible by x
2
+1.
Hard
Solution
verified
Verified by Toppr
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(Bycomparingcoefficients)
⇒a=1,b=7
Hence, a=1 and b=7.
Step-by-step explanation:
please mark me as brilliant
