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obtain all the zeros of the polynomial f x is equal to 2 x ki power 4 plus x ki power 3 minus 14 x ki power 2 - 19 x minus 6 if two of its zeros are minus 2 and -1

Posted by Divakar Singh 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

if -2 and -1 are zeros of f(x) = 2x⁴ + x³ - 14x² - 19x - 6
x+2 and x+1 are factors of f(x)
So (x + 2)(x + 1) = x² + x + 2x + 2 = x² + 3x + 2 is a factor of f(x)

On long division of f(x) by x² + 3x + 2 we get

f(x) = 2x⁴ + x³ - 14x² - 19x - 6 = (2x² - 5x - 3)(x² + 3x + 2)
= (2x + 1)(x - 3)(x + 2)(x + 1)
Therefore, zeroes of the polynomial = {tex}\frac{{ - 1}}{2}{/tex}, 3, -2, -1.

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CBSE > Class 10 > Mathematics