X power 4 +3xpower 3- xsquare …
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Posted by Sravya Grandhi 5 years, 11 months ago
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Sia ? 5 years, 11 months ago
The given polynomial f(x) = x4 - 3x3 - x2 + 9x - 6
Since, two of the zeroes of polynomial are −√3 and √3
hence (x+√3)(x-√3)=x2-3 is a factor of f(x)
Now on long division of f(x) by x2-3
So, f(x) = x4 - 3x3 - x2 + 9x - 6 = (x2 - 3)(x2 - 3x + 2)
= (x + √3)(x - √3)(x2 - 2x - 1x + 2)
= (x + √3)(x - √3)(x - 1)(x - 2)
f(x)=0 if x=-√3 or x=√3 or x=1 or x=2
Therefore, the zeroes of the polynomial are −√3, √3, 1, 2.
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