Explanation
We must find the equation of a polynomial with the following zeros: -5/4, -2/3 and 2.
(1) The general equation for this polynomial is:
[tex]f(x)=a\cdot(x-x_1)\cdot(x-x_2)\cdot(x-x_3).[/tex]
Where x₁, x₂ and x₃ are the zeros.
(2) Replacing the zeros from above, we have:
[tex]f(x)=a\cdot(x+\frac{5}{4})\cdot(x+\frac{2}{3})\cdot(x-2).[/tex]
(3) Expanding the last expression, we have:
[tex]f(x)=a\cdot(x^3-\frac{1}{12}x^2-3x-\frac{5}{3}).[/tex]
(4) Comparing the last expression with the possibilities that we have as answers, we see that a = 12. Replacing this number in the expression above, we get:
[tex]f(x)=12x^3-x^2-36x-20.[/tex]Answer
D.
[tex]f(x)=12x^3-x^2-36x-20.[/tex]
