How do you solve #x^2-3x>=10# using a sign chart?

1 Answer
Dec 11, 2016

Answer:

The answer is #x in ] -oo,-2 ] uu [5, +oo[#

Explanation:

Let's rewrite the equation

#x^2-3x-10>=0#

Let #f(x)=x^2-3x-10=(x+2)(x-5)#

The domain of #f(x)# is #D_f(x)=RR#

Let's do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-2##color(white)(aaaa)##5##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x-2##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-5##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

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

So,

#f(x)>=0# when #x in ] -oo,-2 ] uu [5, +oo[#