The given function is that is a cubic polynomial
[tex]f(x)=-12-2.1x+18x^2-2.75x^3[/tex]
when arranged in descending order that is from highest degree to lowest degree
[tex]f(x)=-2.75x^3+18x^2-2.1x-12[/tex]
Since it is a three degree polynomial it has three roots.
According to rational root theorem , the possible roots of the above expression that is factors of [tex]\frac{12}{2.75}[/tex]=[tex]\frac{48}{11}[/tex] are [tex]\pm1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24, \pm 48, \pm\frac{1}{11}, \pm\frac{2}{11}, \pm\frac{3}{11}\pm\frac{4}{11}\pm\frac{6}{11},\pm\frac{8}{11},\pm\frac{12}{11}, \pm\frac{24}{11},\pm\frac{48}{11}[/tex]
As you can see from the graph all roots of this polynomial are real.
The smallest positive root is 0.954 and smallest negative root are -0.724.
