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By quadratic formula,x=\frac {b^2\pm\sqrt{b^2-4ac}}{2a}. hence if you want roots of opposite sign, then b^2-4ac \ge b^2 => 4ac \le 0 => ac\le 0.
therefore k^2-3k+2\le 0 => (k-1)(k-2) \le 0 => 1\le k \le 2.
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