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If the polynomial x4 - 6x3 + 16x2 - 25x + 10 is divided by another polynomial x2 - 2x + k, the remainder comes out to be x + a, find k and a.
The given polynomial is p(x) = x4 - 6x3 + 16x2 - 25x + 10
Let us divide and equate the obtained remainder with (x + a)
Now, it is given that p(x) when divided by x2 – 2x + k leaves (x + a) as remainder.
Let us equate the remainder with x + a (as given in the question)
(-9 + 2k)x + 10 - 8k + k2 = x + a
Let us compare the coefficient of both LHS and RHS.
-9 + 2k = 1
⇒ 2k = 10
⇒ k = 5 ----- (1)
Also, 10 - 8k + k2 = a ----- (2)
As we obtained the value of k, let us substitute in equation (2) to find the value of a.
a = 10 - 40 + 25
a = - 5
Therefore, the value of k is 5 and a is - 5.
If the polynomial x⁴ - 6x³ + 16x² - 25x + 10 is divided by another polynomial x² - 2x + k, the remainder comes out to be x + a, find k and a.
NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.4 Question 5
If the polynomial x4 - 6x3 + 16x2 - 25x + 10 is divided by another polynomial x2 - 2x + k, the remainder comes out to be x + a. The values of k and a are 5 and - 5 respectively.
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