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Polynomials CBSE NCERT Solutions
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.
Solution: We have P(x) = x4 – 6x3 + 16x2 - 25x + 10
And remainder = x + a.
Now we can divide P(x) = x4 – 6x3 + 16x2 - 25x + 10 by x2 – 2x + k.
According to question
(-9 + 2k)x + 10 – 8k + k2 = + a
On comparing the like coefficients, then we have
-9 + 2k = 1 and 10 – 8k + k2 = a
⇒ –10 + 2k = 0 and 10 – a – 8k + k2 = 0
⇒ k = 10/2 = 5 and 10 – a – 8 (5) + 52 = 0
⇒ k = 5 and – a – 5 = 0
⇒ k = 5 and a = –5
Hence, k = 5 and a = -5.
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