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

1 Answer
Jan 19, 2017

Answer:

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

Explanation:

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 [#