Advanced MathHardProduct of the solutions of a squared-binomial equation
Advanced Math practice question
What is the product of the solutions of the equation (x − 4)² = 2x − 5?
Answer: 21
Expand: x² − 8x + 16 = 2x − 5 → x² − 10x + 21 = 0 → (x − 3)(x − 7) = 0. The solutions are 3 and 7, whose product is 21.
Common wrong answers
- If you answered 10
- 10 is the sum of the solutions.
- If you answered 11
- 11 comes from 16 − 5, before moving all terms to one side.
- If you answered -21
- −21 has the wrong sign; the constant term of x² − 10x + 21 is +21.
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