Advanced MathVery hardQuadratic inequality: where an expression is negative
Advanced Math practice question
For which values of x is x² − 6x + 8 < 0?
- A. 2 < x < 4Correct
- B. x < 2 or x > 4
- C. x < 4
- D. x > 2
Answer: A. 2 < x < 4
x² − 6x + 8 = (x − 2)(x − 4), which is negative exactly between its zeros, 2 and 4.
Why the other answers are wrong
- B. x < 2 or x > 4
- Outside the zeros the product of two same-sign factors is positive.
- C. x < 4
- x < 2 makes both factors negative and the product positive.
- D. x > 2
- x > 4 makes the product positive.
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