How do you solve $9x^2+3x-2>=0$ using a sign chart?

Question

1824 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-13T16:19:20

The answer is $x in ] -oo,-2/3 ] uu [1/3, +oo[$

Let's factorise the LHS

$9x^2+3x-2=(3x-1)(3x+2)$

Let $f(x)=(3x-1)(3x+2)$

Now we can make the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaaaa)$ $-oo$ $color(white)(aaaa)$ $-2/3$ $color(white)(aaaaaa)$ $1/3$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $3x+2$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaaaa)$ $+$

$color(white)(aaaa)$ $3x-1$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaaaa)$ $+$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaaa)$ $+$

Therefore,

$f(x)>=0$ , when $x in ] -oo,-2/3 ] uu [1/3, +oo[$

How do you solve 9x^2+3x-2>=09x^2+3x-2>=0 using a sign chart?