Question

is a polynomial x 4 - 6 x cube + 16 X square - 25 x + 10 is divided by another polynomial x square - 2 X + ki the remainder comes out to X + a find kand a​

Answer 1

Step-by-step explanation:

We know that,

Dividend = Divisor × Quotient + Remainder

⇒ Dividend – Remainder = Divisor × Quotient

⇒ Dividend – Remainder is always divisible by the divisor.

Now, it is given that f(x) when divided by x2 – 2x + k leaves (x + a) as remainder.

So, for f(x) to be completely divisible by x2 – 2x + k, remainder must be equal to zero

⇒ (–10 + 2k)x + (10 – a – 8k + k2) = 0

⇒ –10 + 2k = 0 and 10 – a – 8k + k2 = 0

⇒ k = 5 and 10 – a – 8 (5) + 52 = 0

⇒ k = 5 and – a – 5 = 0

⇒ k = 5 and a = –5