16Hit1600
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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