Determine the quadratic equation whose solutions are the reciprocals of the roots of the equation 2x² + 5x + 3 = 0.

Explanation

To find the quadratic equation with roots that are the reciprocals of those of 2x² + 5x + 3 = 0, substitute x with 1/x. This gives 2(1/x)² + 5(1/x) + 3 = 0. Multiplying through by x² yields 2 + 5x + 3x² = 0, which rearranges to 3x² + 5x + 2 = 0. However, the correct form with roots as reciprocals is obtained by multiplying the original equation by x² and rearranging properly, leading to 3x² + 5x - 2 = 0.