Question

Determine the roots of f(x) = -12-2.1x+18x^2-2.75x^3 graphically. in addition, determine the first root of the function with

Answer 1

The given function is that is a cubic polynomial

$f(x)=-12-2.1x+18x^2-2.75x^3$

when arranged in descending order that is from highest degree to lowest degree

$f(x)=-2.75x^3+18x^2-2.1x-12$

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  $\frac{12}{2.75}$=$\frac{48}{11}$  are $\pm1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24, \pm 48, \pm\frac{1}{11}, \pm\frac{2}{11}, \pm\frac{3}{11}\pm\frac{4}{11}\pm\frac{6}{11},\pm\frac{8}{11},\pm\frac{12}{11}, \pm\frac{24}{11},\pm\frac{48}{11}$

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.