CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
The sum of a number and its reciprocal is 5/2. Which of the following gives both possible values of the number?
The number is either 2 or 1/2. Writing x + 1/x = 5/2 and clearing fractions gives 2x² − 5x + 2 = 0, which factorises as (2x − 1)(x − 2) = 0. Both values give a sum of 5/2 with their reciprocals.
- A2 and 1/2Correct
- B5 and 1/5
- C3 and 1/3
- D1 and 3/2
Explanation
Let the number be x: x + 1/x = 5/2, so 2x² − 5x + 2 = 0. Factorising gives (2x − 1)(x − 2) = 0, so x = 1/2 or 2. Check: 2 + 1/2 = 5/2. The pair 5 and 1/5 sums to 26/5, so it is wrong.
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