polynomials

Asked by hemant2020 | 20th May, 2010, 09:30: PM

Expert Answer:

Dear Student

When x4 - 6 x3 +16x2 - 25x +10 is divided by x2 - 2x +k, the quotient we get is x2 - 4x +(8-k); and the remainder is [(2k-9)x+(k2-8k+10)].

The remainder given in question is x+a. Equating the the given and the obtained remainder, we get:

(2k-9)x+(k2-8k+10) = x + a

Equating the coefficient of x,

2k-9=1

k=5

Similarly equating the constant term, and substituting the value k=5 it,

k2-8k+10= a

52-8*5+10 = a

a=-5

Regards Topperlearning.

 

Answered by  | 29th May, 2010, 11:39: AM

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