Q. 54.4( 406 Votes )
If the polynomial x4 - 6x3 + 16x2 - 25x + 10 is divided by another polynomial x2 - 2k + k the remainder comes out to be x + a, find k and a.
To solve this question divide x4 - 6 x3 + 16 x2 - 25 x + 10 by x2 - 2 x + k by long division method
Let us divide, by
So, remainder = (2k - 9)x + (10 - 8k + k2)
But given remainder = x + a
⇒ (2k - 9)x + (10 - 8k + k2) = x + a
Comparing coefficient of x, we have
2k - 9 = 1
⇒ 2k = 10
⇒ k = 5
Comparing constant term,
10 - 8k + k2 = a
⇒ a = 10 - 8(5) + 52
⇒ a = 10 - 40 + 25
⇒ a = -5
So, the value of k is 5 and a is -5.
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