Advanced MathEasy–MediumZeros of a factored quadratic
Advanced Math practice question
The function f is defined by f(x) = (x + 2)(x − 6). For which values of x is f(x) = 0?
- A. −2 and 6Correct
- B. 2 and −6
- C. −2 and −6
- D. 2 and 6
Answer: A. −2 and 6
A product is zero when a factor is zero. x + 2 = 0 gives x = −2, and x − 6 = 0 gives x = 6.
Why the other answers are wrong
- B. 2 and −6
- The signs are reversed. Setting x + 2 = 0 gives x = −2 (not 2), and x − 6 = 0 gives x = 6 (not −6).
- C. −2 and −6
- x − 6 = 0 when x = 6, not −6. Only the first factor produces a negative zero.
- D. 2 and 6
- x + 2 = 0 when x = −2, not 2. Each factor is solved by making the bracket zero, which flips the sign of the number inside.
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For x ≠ 0, which expression is equivalent to (x² + 3x) / x? - Easy–Medium
What are the solutions to the equation 2(x − 3)² − 32 = 0 ?
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