Question

If the polynomial x⁴- 6x³- 16x² - 25 x + 10 is divided by (x²-2x + k )
the remainder comes
out to
be (x + a). Find k and a​

Answer 1

Answer:

On dividing x4 - 6x3 - 16x2 - 25x + 10 by x2 - 2x +

∴ Remainder = (2k - 9)x - (8 - k)k + 10

But the remainder is given as x+a.

On comparing their coefficients,

2k - 9 = 1

⇒ k = 10

⇒ k = 5 and,

-(8 - k)k + 10 = a

⇒ a = -(8 - 5)5 + 10 = -15 + 10 = -5

Hence, k = 5 and a = -5

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Answer 2

ANSWER:

K=5,A=-5

Step-by-step explanation:

On dividing x4 - 6x3 - 16x2 - 25x + 10 by x2 - 2x + k

∴ Remainder = (2k - 9)x - (8 - k)k + 10

But the remainder is given as x+a.

On comparing their coefficients,

2k - 9 = 1

⇒ k = 10

⇒ k = 5 and,

-(8 - k)k + 10 = a

⇒ a = -(8 - 5)5 + 10 = -15 + 10 = -5

Hence, k = 5 and a = -5