Question

Find the value of a and b if (x2+1) is a factor of the polynomial x4+x3+8x2+ax+b

Answer 1

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Answer 2

Given : p(x)=$x^4+x^3+8x^2+ax+b$

g(x) = $x^2+1$

To find: a and b

Explanation:

on dividing $x^4+x^3+8x^2+ax+b$ by $x^2+1$

we get

quotient = x²+x+7

Remainder = (a-1)x+(b-7)

Since , it s given that g(x) is the factor of p(x)

so the remainder must be equal to 0

(a-1)x+(b-7)=0

on comparing the coefiicients

a-1 = 0

a = 1

b-7 = 0  

b= 7

thus , the value is a =1  and b = 7

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