Advanced MathMediumInterval where a factored quadratic is negative
Advanced Math practice question
The function f is defined by f(x) = (x − 1)(x − 5). For which values of x is f(x) less than 0?
- A. 1 < x < 5Correct
- B. x < 1 or x > 5
- C. x < 5
- D. x > 1
Answer: A. 1 < x < 5
The product of (x − 1) and (x − 5) is negative exactly when one factor is negative and the other positive: between the zeros, 1 < x < 5.
Why the other answers are wrong
- B. x < 1 or x > 5
- Outside the zeros both factors have the same sign, so f(x) > 0.
- C. x < 5
- For x < 1 both factors are negative and f(x) > 0.
- D. x > 1
- For x > 5 both factors are positive and f(x) > 0.
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