Question

the polynomial x4-6x3+16x2-25x+10 is divided by x2-2x+k the remainder comes out to be x+a,find k and a​

Answer 1

The value of k and a is 5 and -5 respectively.

Step-by-step explanation:

\frac{\left[x^{4}-6 x^{3}+16 x^{2}-25 x+10\right]}{\left[x^{2}-2 x+k\right]}

[x

2

−2x+k]

[x

4

−6x

3

+16x

2

−25x+10]

and reminder = x+a

On diving the above given equation, we get ,

Given the reminder is (x+a)

(4k-25+16-2k)x+[10-k(8-k)] = x+a

(2 k-9) x+\left[10-8 k+k^{2}\right]=x+a(2k−9)x+[10−8k+k

2

]=x+a

On comparing on both sides, we get

2k-9=1

2k=10

Therefore, k=5

Also, 10-8 k+k^{2}=a10−8k+k

2

=a

10-8(5)-5^{2}=a10−8(5)−5

2

=a

10-40+25=a

Therefore, a=-5

Answer 2

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