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| 1. |
X power 4 +3xpower 3- xsquare -9x -6 ÷ xsquare -3 |
| Answer» The given polynomial f(x) = x4 - 3x3 - x2 + 9x - 6Since, two of the zeroes of polynomial are {tex}- \\sqrt 3{/tex}\xa0and {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\xa0x2-3So, f(x) = x4 - 3x3\xa0- x2 + 9x - 6 = (x2 - 3)(x2 - 3x + 2)= (x + {tex}\\sqrt 3{/tex})(x - {tex}\\sqrt 3{/tex})(x2 - 2x - 1x\xa0+ 2)= (x + {tex}\\sqrt 3{/tex})(x - {tex}\\sqrt 3{/tex})(x - 1)(x - 2)f(x)=0 if x=-{tex}\\sqrt 3{/tex}\xa0or x={tex}\\sqrt 3{/tex}\xa0or x=1 or x=2Therefore, the zeroes of the polynomial are {tex}-\\sqrt 3{/tex}, {tex}\\sqrt 3{/tex}, 1, 2. | |