Proof: the equation (x-1) (X-2) = m has two unequal real roots
It is proved that: (x-1) (X-2) = M & # 178;
x²-3x+2-m²=0
Discriminant = 9-4 (2-m & # 178;) = 4m & # 178; + 1
Because 4m & # 178; > = 0
So 4m & # 178; + 1 > 0
So there are always two unequal real roots
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