2x² - 3x + 1 = 0
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 x₂ = 1
2x/2 = 1/2
x₁ = 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:
x₁ = 2 x₂ = 1
x² - (sum of roots)x + (product of roots) = 0
x² - [(2) + (1)]x + [(2)(1)] = 0
x² - 3x + 2 = 0
ANSWER: x² - 3x + 2 = 0
