16Hit1600
Advanced MathVery hardInterval where a quadratic is negative

Advanced Math practice question

For which values of x is p(x) = x² − 8x + 7 negative?

  1. A. 1 < x < 7Correct
  2. B. x < 1 or x > 7
  3. C. −7 < x < −1
  4. D. 0 < x < 8

Answer: A. 1 < x < 7

p(x) = (x − 1)(x − 7), which is negative between its zeros.

Why the other answers are wrong

B. x < 1 or x > 7
That is where p(x) is positive.
C. −7 < x < −1
The zeros are 1 and 7, not −1 and −7.
D. 0 < x < 8
0 and 8 give p = 7, which is positive.

More Advanced Math questions

Not affiliated with the College Board. SAT is a trademark of the College Board.