Between what two positive integers does x^3 + 3x^2+ 4x - 9 = 0 have an irrational root?

Question

amistre64 · Answer

setup a trial and error table of integers inputs; when you swap signs, you know that there must be some fractional solution between the integers

amistre64 · Answer

you could develop a pool of rational solutions to test out as well; using the rational roots thrm

anonymous · Answer

@amistre64 What do you mean?

amistre64 · Answer

sites getting a little wonky :/

there is a thrm pertaining to rational roots;  IF a polynomial has rational roots then they must consist of the factors of the first and last coefficients:  last/first i believe

amistre64 · Answer

since 9 has the factors of:  1,3,9
and 1 has the factors of :   1

this simplifies our trial and error pool to:

x = -3,-9,-1,1,3,9

if the value of the poly goes form + to -, or from - to +, then it must have crossed over the x axis at some point between the trials

amistre64 · Answer

find the values of your equation with those x values and tell me what we get

anonymous · Answer

@amistre64 I tried all of them, but none of them works.