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If the polynomial x4-6x3+16x2-25x+10 is divided …

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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.

Posted by Sukhman Kang 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

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

{tex}\therefore{/tex} Remainder = (2k - 9)x - (8 - k)k + 10
But the remainder is given as x+a.
On comparing their coefficients,
2k - 9 = 1
{tex}\Rightarrow{/tex} k = 10
{tex}\Rightarrow{/tex} k = 5 and,
-(8 - k)k + 10 = a
{tex}\Rightarrow{/tex} a = -(8 - 5)5 + 10 = -15 + 10 = -5
Hence, k = 5 and a = -5

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