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| 1. |
Obtain all the zeros of x4+5x3-2x2-40x-8 if two of its zeroes are 2root2 and -2root 2 |
| Answer» We have two zeros\xa0{tex}\\sqrt { 2 }\\; \\text { and } - \\sqrt { 2 }{/tex}{tex}\\therefore{/tex}Two factors are (x +\xa0{tex}\\sqrt 2{/tex}\xa0) and (x - {tex}\\sqrt 2{/tex}\xa0)g(x) = (x + {tex}\\sqrt 2{/tex}\xa0) (x - {tex}\\sqrt 2{/tex}\xa0) = x2 - 2 is a factor of the given polynomialQuotient = x2\xa0- 5x + 4 = (x - 4)(x - 1)Hence, other zeroes are 4 and 1. | |