Question

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

Answer 1

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

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