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Addition and Subtraction of a Matrix

Find the valu...

Question

Find the value of a and b so that x⁴+ x³+ 8x²+ax+ b is divisible by . x²+1.

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Solution

Let p(x)=x⁴ +x³+ 8x²+ax+b=0
x²+1=0
∴x=+-1
therefore,p(1)=1+1+8+a+b=0
=10+a+b=0
=a+b=-10------(1)
p(-1)=1-1+8-a+b=10
=-a+b=-8------(2)
(1)+(2), a+b=-10
-a+b=-8
________
2b=-18
b=-9---------(3)
(3) in (1),a-9=-10
a=-1
therefore the values of a and b are -9 ans -1

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