Question

x 4 + x cube + ax square + b is exactly divisible by x square + 1 find the values of a and b​

Answer 1

Answer:

Step-by-step explanation:

Let us first divide the given polynomial x  4 +x  3 +8x  2 +ax+b by (x  2  +1)

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.