If x²+1 is the factor of x⁴+x³-8x²+ax+b1 then find the value of a and b
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Heya user,
Let's say... --> x² + 1 = 0
=========> x = + i or - i are the only possible soln.
By factor theorem, if ( x - a ) is a factor of f(x), f(a) = 0;
Soo, f(i) = 1 - i + 8 + ai + b = 0
=====> ai + b = 9 - i --> (i)
--> f ( -i ) = 1 + i + 8 - ai + b = 0
=====> ai - b = 9 + i --> (ii)
From (i) and (ii),
----> 2ai = 18 => a = 9/i = -9i => b = -i
=> (a,b) = (-9i , -i)
Let's say... --> x² + 1 = 0
=========> x = + i or - i are the only possible soln.
By factor theorem, if ( x - a ) is a factor of f(x), f(a) = 0;
Soo, f(i) = 1 - i + 8 + ai + b = 0
=====> ai + b = 9 - i --> (i)
--> f ( -i ) = 1 + i + 8 - ai + b = 0
=====> ai - b = 9 + i --> (ii)
From (i) and (ii),
----> 2ai = 18 => a = 9/i = -9i => b = -i
=> (a,b) = (-9i , -i)
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