Question

if x4 -2x3 +6x2 -6x+k completely divisible by x2-2x +3 then find the value of k

Answer 1

hey mate here is your answer

x4-2x3 + 6x2-6x+k =0 only if x is the value got by factorizing the x2-2x+3
so x2-3x+x-3
x(x-3)+1(x -3)
so (x+3)(x+1)=0
x = -3 or x = -1

so when we substitute x value we get
if x= -1
1-6-12+6+k =0
-13+k =0
k = 13

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