How do you solve #x^2-10<3x#?

1 Answer
Nov 26, 2016

Answer:

THe answer is #x in ] -2,5 [ #

Explanation:

Let's rewrite the equation as

#f(x)=x^2-3x-10=(x+2)(x-5)<0#

Let's do a 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# for #x in ] -2,5 [ #

graph{x^2-3x-10 [-25.66, 25.65, -12.83, 12.85]}