Obtain all the zeroes of polynomial …
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Sia ? 6 years, 6 months ago
The given polynomial f(x) = x4 - 3x3 - x2 + 9x - 6
Since, two of the zeroes of polynomial are {tex}- \sqrt 3{/tex} and {tex}\sqrt 3{/tex}
hence (x+{tex}\sqrt 3{/tex})(x-{tex}\sqrt 3{/tex})=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 + {tex}\sqrt 3{/tex})(x - {tex}\sqrt 3{/tex})(x2 - 2x - 1x + 2)
= (x + {tex}\sqrt 3{/tex})(x - {tex}\sqrt 3{/tex})(x - 1)(x - 2)
f(x)=0 if x=-{tex}\sqrt 3{/tex} or x={tex}\sqrt 3{/tex} or x=1 or x=2
Therefore, the zeroes of the polynomial are {tex}-\sqrt 3{/tex}, {tex}\sqrt 3{/tex}, 1, 2.
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