How do you solve $x^2-3x>54$ using a sign chart?

Question

1705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-19T17:38:01

The answer is $x in ] -oo,-6 [ uu ] 9, oo [$

Let's rewrite the inequality

$x^2-3x-54>0$

Let's factorise

$x^2-3x-54=(x+6)(x-9)$

and let $f(x)=x^2-3x-54$

Now we can make the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-6$ $color(white)(aaaa)$ $9$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $x+6$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x-9$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

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

Therefore,

$f(x)>0$ , when $x in ] -oo,-6 [ uu ] 9, oo [$

How do you solve x^2-3x>54x^2-3x>54 using a sign chart?