Answer:
C. f(x) = 2x⁴ +6x³ +22x² +54x +36
Explanation:
You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.
Y-intercept
The given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.
Rule of signs
Descartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.
Given roots
The given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.
f(x) = 2x⁴ +6x³ +22x² +54x +36