find the x-intercepts of -4x^3 + 6x^2

[AGlas9837]

I'm trying to find the x-intercept(s) of -4x^3 + 6x^2 (and then determine y sign chart).

Factoring, I get -3/2 and 0. From the interval (- infinity to -3/2), the sign is positive and from (-3/2 to 0) and (0 to 3/2) these intervals are also positive. But testing (3/2 to infinity) this interval is negative so it appears that 3/2 is also an x-intercept although I don't see how. Are these the correct x-intercepts?

 

[soroban]

Re: X-intercepts

Hello, AGlas9837!

Check your algebra . . .

Find the x-intercept(s) of: \(\displaystyle -4x^3 + 6x^2\) ... and determine y sign chart.

\(\displaystyle \text{We have: }\;-4x^3 + 6x^2 \;=\;0\)

\(\displaystyle \text{Factor: }\;2x^2(-2x + 3) \;=\;0\)

\(\displaystyle \text{Then: }\;\begin{array}{ccccccccc}2x^2 &=&0 & &\Rightarrow && x &=&0 \\ \text{-}2x+3 &=&0 && \Rightarrow& & x &=&\frac{3}{2} \end{array}\)

 

[AGlas9837]

Thank you! Somewhere I'd seen or read that you should factor out -1, so I wasn't sure if one of the x-intercepts wasn't +3/2.

 

[AGlas9837]

Sorry...meant negative 3/2.