Advanced MathHardRational equation that becomes a quadratic
Advanced Math practice question
If x + 6/x = 5 and x ≠ 0, what is the product of all the solutions to the equation?
Answer: 6
Multiply by x: x² + 6 = 5x, so x² − 5x + 6 = 0, which factors as (x − 2)(x − 3) = 0. The solutions are 2 and 3; their product is 6.
Common wrong answers
- If you answered 2
- 2 is one solution; the other is 3. Multiply them.
- If you answered 5
- 5 is the SUM of the solutions (2 + 3). The question asks for the product.
- If you answered -6
- −6 has the wrong sign; the constant term of x² − 5x + 6 is +6, which equals the product of the roots.
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