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skeeter · #6 December 3rd, 2008, 04:56 PM

$f(x) = k(x - r_1)(x - r_2)$

$f(x) = k[x^2 -(r_1 + r_2)x + r_1 \cdot r_2]$

$r_1 + r_2 = (2 - \sqrt{3}) + (2 + \sqrt{3}) = 4$

$r_1 \cdot r_2 = (2 - \sqrt{3})(2 + \sqrt{3}) = 4 - 3 = 1$

$f(x) = k(x^2 - 4x + 1)$

since $f(1) = -2$

$-2 = k[(1)^2 - 4(1) + 1]$

$-2 = k(-2)$

$k = 1$

so ...

$f(x) = x^2 - 4x + 1$

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