Question

x intercept for this function

Answer 1

\[\huge y=x^3-9x^2+15x+4\]

Answer 2

this is unfactorable?

Answer 3

oh no wait nevermind

Answer 4

Any particular method they want you to use? Do they specify factoring?

Answer 5

No but isnt that the only way?

Answer 6

Graphing is the easiest.

Answer 7

Graph that bad boy. Look for where it crosses the x axis. Doneso.

Answer 8

no i have to use an algebraic method

Answer 9

because like say on an exam, i cant graph that

Answer 10

Possible rational roots are :

Answer 11

Okay then your best best is to use the rational root theorem to list possible rational roots. Then check each one to see if it is a valid root.

Answer 12

\[\pm1,\pm4,\pm2\]

Answer 13

Use synthetic division to see if any of those are actual roots.

Answer 14

Mertsj is correct. The way he got those possible roots is:
A: Make a list of factors for the last number (In this case, it's 4)
B: Make a list of factors for the first coefficient (In this case, it's 1)

Possible rational roots must be of the form \(\huge \frac{\text{things in the first list}}{\text{things in the second list}}\)

Answer 15

It is not factorable.

Answer 16

So the best approach would be to find where y changes sign. Then you would know there is a root between those two values and you could hone in on it by trial and error. Of if you know calculus, you could use the derivative. What class is this for?

Answer 17

@Mertsj calculus !

Answer 18

they want you to bruteforce using newton's more than likely