Question

if the polynomial X4-6X3+16X2-25X+10 is divided by poynomial X2-2X+k the remainder come out to be X+a find k and a ​

Answer 1

Step-by-step explanation:

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Answer 2

Correct question :-

If the polynomial x^4 - 6x³ + 16x² - 25x + 10 is divided by poynomial x² - 2x + k the remainder come out to be x + a find k and a .

Solution :-

First calculate the remainder in terms of k by dividing x^4 - 6x³ + 16x² - 25x + 10 by x² - 2x + k and equate to the remainder (x + a)

[ Refer to attachment for division ]

From attachment, We obtained the remainder as - 9x + 2x + k² - 8x + 10

Also, in the question remainder is given as x + a

Equating both we get,

⇒ x + a = - 9x + 2kx + k² - 8k + 10

⇒ x + a = x(-9 + 2k) + k² - 8k + 10

Comparing on both sides, we get

• x =x( - 9 + 2k)
• a = k² - 8k + 10

Solving x = x(- 9 + 2k)

⇒ x = x(-9 + 2k)

⇒ 1 = - 9 + 2k

⇒ 1 + 9 = 2k

⇒ 10 = 2k

⇒ 10/2 = k

⇒ k = 5

Substituting k = 5 in a = k² - 8k + 10

⇒ a = 5² - 8(5) + 10

⇒ a = 25 - 40 + 10

⇒ a = 35 - 40 = - 5

Therefore the value of k is 5 and the value of a is - 5.