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Write the quadratic equation with integer coefficents whose roots are the reciprocal of the roots of 2x^2-3x+1=0...

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A) Solve for the roots. Solve by factoring:

2x² - 3x + 1 = 0

(2x - 1) (x - 1) = 0

2x - 1 = 0 x - 1 = 0

2x - 1 + 1 = 0 + 1 x - 1 + 1 = 0 + 1

2x = 1

2x/2 = 1/2

The roots and their reciprocals are:

x₁ = 1/2 Reciprocal: x₁ = 2/1 or 2

x₂ = 1 Reciprocal: x₂ = 1

B) Quadratic equation given the reciprocal of the roots of the first equation:

x² - (sum of roots)x + (product of roots) = 0

x² - [(2) + (1)]x + [(2)(1)] = 0

x² - 3x + 2 = 0