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Answer:
x^2 -5x +6 = 0
Step-by-step explanation:
Perhaps the easiest way to do this is to find the roots of the given equation, then write the equation that has reciprocal roots. The given equation can be factored as ...
(2x -1)(3x -1) = 0 ⇒ roots 1/2, 1/3
Then the factoring of the equation with reciprocal roots is ...
(x -2)(x -3) = 0
x^2 -5x +6 = 0
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If p is a root, then (x -p) is a factor. If (ax -b) is a factor, then b/a is a root, the value of x that makes that factor zero.
