16Hit1600
Advanced MathVery hardQuadratic inequality: where an expression is negative

Advanced Math practice question

For which values of x is x² − 6x + 8 < 0?

  1. A. 2 < x < 4Correct
  2. B. x < 2 or x > 4
  3. C. x < 4
  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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