find the value of a and b
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Sneha3123:
i no the answer
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so the answer of the question is a = 1 and b = 7
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Since x 2 + 1 divides x 4 + x 3 + 8x 2 + ax + b , so the quotient will be a polynomial of degree 2.
So, we can write
x 4 + x 3 + 8x 2 + ax + b = (x 2 + 1) (a 1 x 2 + b 1 x + c 1)
? x 4 + x 3 + 8x 2 + ax + b = a 1 x 4 + a 1 x 2 + b 1 x 3 + b 1 x + c 1 x 2 + c 1
? x 4 + x 3 + 8x 2 + ax + b = a 1 x 4 + b 1 x 3 + (a 1 + c 1) x 2 + b1 x + c 1
Comparing the coefficient of x 4 on both sides, we get –
a 1 = 1
On comparing the coefficient of x 3, we get –
b 1 = 1
On comparing the coefficient of x 2, we get –
a 1 + c 1 = 8
? 1 + c 1 = 8
? c 1 = 7
On comparing the coefficient of x on both sides, we get –
a = b 1 = 1
? a = 1
On comparing the constants on both sides, we get –
b = c 1 = 7
? b = 7
hope this will help u
So, we can write
x 4 + x 3 + 8x 2 + ax + b = (x 2 + 1) (a 1 x 2 + b 1 x + c 1)
? x 4 + x 3 + 8x 2 + ax + b = a 1 x 4 + a 1 x 2 + b 1 x 3 + b 1 x + c 1 x 2 + c 1
? x 4 + x 3 + 8x 2 + ax + b = a 1 x 4 + b 1 x 3 + (a 1 + c 1) x 2 + b1 x + c 1
Comparing the coefficient of x 4 on both sides, we get –
a 1 = 1
On comparing the coefficient of x 3, we get –
b 1 = 1
On comparing the coefficient of x 2, we get –
a 1 + c 1 = 8
? 1 + c 1 = 8
? c 1 = 7
On comparing the coefficient of x on both sides, we get –
a = b 1 = 1
? a = 1
On comparing the constants on both sides, we get –
b = c 1 = 7
? b = 7
hope this will help u
put the value in x^4+x^3+8x^2+ax+b and then divide by x^2+1
Answer a is 1 and b is 7
thnx i got my mistake
u should tell me that √-1 ≠ 1
but now i answered it by another method
tell us
how to find the value of a and b
i have written it in my answer
thanks
ur welcome
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