Question

Find the values of ‘a’ and ‘b’ so that x
4 + x
3 + 8x
2 + ax + b is divisible by x
2 + 1

Answer 1

Answer:

a = 2 b = -1/2

Step-by-step explanation:

calculate by using factoer theorem

Answer 2

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 x2 +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.