How do you solve (x+5)(x-2)>=0(x+5)(x2)0?

1 Answer
Dec 20, 2016

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

Explanation:

Let f(x)=(x+5)(x-2)f(x)=(x+5)(x2)

Now, we can do a sign chart

color(white)(aaaa)aaaaxxcolor(white)(aaaa)aaaa-oocolor(white)(aaaa)aaaa-55color(white)(aaaa)aaaa22color(white)(aaaa)aaaa+oo+

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

color(white)(aaaa)aaaax-2x2color(white)(aaaaa)aaaaa-color(white)(aaaa)aaaa-color(white)(aaaa)aaaa++

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

Therefore,

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

graph{(x+5)(x-2) [-28.86, 28.85, -14.43, 14.43]}