Advanced MathHardProduct of the solutions of a rational equation
Advanced Math practice question
The equation 2/x = x − 1 has two solutions. What is the product of the solutions?
Answer: -2
Multiply by x: 2 = x² − x → x² − x − 2 = 0 → (x − 2)(x + 1) = 0. The solutions are 2 and −1, whose product is −2.
Common wrong answers
- If you answered 1
- 1 is the sum of the solutions.
- If you answered 2
- 2 has the wrong sign; the product of the roots of x² − x − 2 is −2.
- If you answered -1
- −1 is one solution alone.
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