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
`(12)/(2.75)`=
`(48)/(11)` are
`\pm1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24, \pm 48, \pm(1)/(11), \pm(2)/(11), \pm(3)/(11)\pm(4)/(11)\pm(6)/(11),\pm(8)/(11),\pm(12)/(11), \pm(24)/(11),\pm(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.