Question

solve -3x^2+6x+2≥0 can you please show me how to solve it thanks

Answer 1

so we have
\[3x^2-6x-2 \le 0\]
\[\text{ let } f(x)=3x^2-6x-2\]
we need to find when f is 0 first
\[3x^2-6x-2=0\]
we need to solve this equation for x
\[x=\frac{-(-6) \pm \sqrt{(-6)^2-4(3)(-2)}}{2(3)}=\frac{6 \pm \sqrt{36+24}}{6}=\frac{6 \pm \sqrt{60}}{6}\]
\[x=\frac{6 \pm 2 \sqrt{15}}{6}=\frac{6}{6} \pm \frac{2 \sqrt{15}}{6}=1 \pm \frac{\sqrt{15}}{3}\]

so we have

I chose in a number in each of the intervals divided by the zeros of f
so do f(3); f(0); f(-1)