PSAT Math Multiple-Choice Question 590: Answer and Explanation

Question: 590

The function y = 6x³ + 19x² - 24x + c has zeros at the values of , and -4. What is the value of the constant c in this function

• A. -16
• B. -9
• C. 2
• D. 14

Correct Answer: A

Explanation:

(A) Plug in one of the zeros for x and plug in the number 0 for y since a zero intersects the x-axis. Remember that the y-value must be 0 for an x-intercept since that indicates where the function intersects the x-axis. Use this to solve for the constant c. Use -4 as that x-value so that you do not have to calculate with fractions:

y = 6x³ + 19x² - 24x + c

0 = 6(-4)³ + 19(-4)² - 24(-4) + c

0 = 6(-64) + 19(16) + 96 + c

0 = -384 + 304 + 96 + c

0 = 16 + c

-16 = c