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find the value of k for which the polynomial x 4 + 10 x cube + 25 x square + 15 X + K is exactly divisible by X + 7

Posted by Vaibhav Tripathi 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have to find the value of k for which x⁴ + 10x³ + 25x² + 15x + k is exactly divisible by x + 7.

If x + 7 is a factor then (-7) is a root.
So f(-7) = (-7)⁴ + 10 (-7)³ + 25(-7)² + 15(-7) + k = 0
2401 - 3430 + 1225 -105 + k = 0
or, 3626 - 3535 + k = 0
or, 91 + k = 0
{tex}\therefore{/tex}k = -91

0Thank You

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CBSE > Class 10 > Mathematics