Question

Is 1 the x-intercept for:

f(x)=x^3-1/x^2-x

Answer 1

Hint:

x^3-1 = (x-1)(x^2 + x + 1)

Answer 2

so there is no x-intercept

Answer 3

what makes you say that

Answer 4

x can never = 0

Answer 5

true, but that doesn't mean we won't have x-intercepts

Answer 6

=/

Answer 7

can you simplify (x^3-1)/(x^2-x)

Answer 8

would x^2 cancel out and be left with x-1/-x?

Answer 9

no

Answer 10

x^3-1 = (x-1)(x^2 + x + 1)

x^2-x = x(x-1)

Answer 11

what cancels?

Answer 12

x+1 and x-1

Answer 13

you mean the two x-1 terms right?

Answer 14

correct

Answer 15

so you're left with


x^2 + x + 1
-----------
x

Answer 16

set that whole thing equal to 0 and solve for x

Answer 17

i see...wouldn't this also mean there would be a Rational discontinuity?

Answer 18

there is a discontinuity and it's at x = 0 since x can't be 0

Answer 19

would i have to use the quadratic formula on x^2+x+1 in order to find an x-intercept?

Answer 20

yes, that's the most direct way to do so (since factoring involves guessing)

Answer 21

this would give me an imaginary number though correct?

Answer 22

that is correct

Answer 23

so there are no real x intercepts

Answer 24

awesome! thanks for the help!

Answer 25

np