SAT Math Multiple Choice Question 615: Answer and Explanation

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Question: 615

15. The function g(x) = ax3 + bx2 + cx + d has zeroes at x = -2, x = 3, and x = 6. If g(0) < 0, which of the following must also be negative?

  • A. g(-3)
  • B. g(-1)
  • C. g(4)
  • D. g(5)

Correct Answer: B

Explanation:

B

Advanced Mathematics (analyzing polynomial functions) HARD

Because this polynomial has a degree of 3 (which is the highest power of any of its terms), it cannot have more than 3 zeros. These three zeros are given as -2, 3, and 6. We also know that g(0), the y-intercept of the graph, is negative. This gives us enough information to make a rough sketch of the graph.

Images

This shows that the only values of x for which the function is negative are -2 < x < 3 and x > 6. Therefore the only negative value among the choices is (B) g(-1).

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