Math, asked by ruhi7156, 10 months ago

obtain all the zeroes of the polynomial x⁴-5x³+3x²+7x-2,if two of its zeroes are (2+root3) (2-root3)​

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Answered by lcisharma
2

   \\   x {}^{4}  -  5x {}^{3} +3x {}^{2}  +  7x - 2 = 0  = p(x)\\ x =  \alpha  =  2  + \sqrt{3}   \\ x = \beta  =  2 -  \sqrt{3}  \\  s =  \alpha   + \beta  = 4 \\ p =  \alpha  \beta  = 1 \\ g(x)  = x {}^{2}  - sx + p \\  = x {}^{2}  - 4x + 1 \\  \\ p(x) \div g(x)

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