Question

Finding polynomial roots (I have 3 questions, will post the first one first)

Answer 1

\[y=3x ^{3}-7x^{2}-14x+24\]

Answer 2

that's the first one =)

Answer 3

\(\Large\color{black}{ \displaystyle y=ax ^{n}+bx^{n-1}+~...~+cx+d }\)

The possible roots are:

\(\Large\color{black}{ \displaystyle x=\pm \frac{\rm ~fractors~of~d~}{a} }\)

Answer 4

\(\Large\color{black}{ \displaystyle y=3x^3-7x^2-14x+24 }\)

The possible roots are:

\(\Large\color{black}{ \displaystyle x=\pm \frac{\rm ~fractors~of~24 ~}{3} }\)

\(\large\color{blue}{ \displaystyle x=\pm \frac{24 }{3},\pm \frac{12}{3},\pm \frac{8}{3},\pm \frac{6}{3},\pm \frac{4}{3},\pm \frac{3}{3},\pm \frac{2}{3},\pm \frac{1}{3}. }\)

Answer 5

I know that it will only have 3 roots because the first term is cubed, but how do I know which roots they are?

Answer 6

Those are all positie roots.
Plug each root and see which 3 roots work. (Can be only 1 or only 2 roots as well)

Answer 7

So I have to plug all of those in (synthetic division) and figure out which three work? Ugh work =P (I know that the answer is -2, 3, and 4/3)

Answer 8

Yes, and these as you can see are 3 of the possible zeros.

Answer 9

theres no short cuts but drawing a graph will help

Answer 10

Okay :) Thank you!