by Integr88 » Thu 31 March, 2011 18:21
When we want to find the x-intercept for an equation, it means to set y=0 and solve for x
we have `y=6x^3+13x^2+2x` so setting y=0 we get: `0=6x^3+13x^2+2x`
Our first step is to factor out x as x is common in all terms and we have`x(6x^2+13x+2)`
Now factor the inside `6x^2+13x+2=(6x+1)(x+2)`
putting them together we have :`x(6x+1)(x+2)` this is the fully factored form where we can find x values.
Now set x=0 and 6x+1=0 and x+2=0 and solve for x and we get:
for x=0 we do not nothing as we have it.
for 6x+1=0. Subtract 1 from both side and we have 6x=-1 and now divide both side by 6 and have: `(6x)/6=-1/6`. the 6 on the left canceles out and we left with:
`x=-1/6`
for x+2=0 just subtract 2 from both side and we have:
x=-2
`:.` the x-intercepts are `0, -1/6 and -2`