How do you solve m^3-2m^2-15m>0 using a sign chart?

1 Answer
Mar 6, 2017

The solution is m in ]-3,0 [uu]5, +oo[

Explanation:

Let's factorise the inequality

m^3-2m^2-15m>0

m(m^2-2m-15)>0

m(m+3)(m-5)>0

Let f(m)=m(m+3)(m-5)

Now, we can build the sign chart

color(white)(aaaa)mcolor(white)(aaaa)-oocolor(white)(aaaa)-3color(white)(aaaa)0color(white)(aaaaa)5color(white)(aaaaa)+oo

color(white)(aaaa)m+3color(white)(aaaaa)-color(white)(aaaa)+color(white)(aaaa)+color(white)(aaaa)+

color(white)(aaaa)mcolor(white)(aaaaaaaa)-color(white)(aaaa)-color(white)(aaaa)+color(white)(aaaa)+

color(white)(aaaa)m-5color(white)(aaaaa)-color(white)(aaaa)-color(white)(aaaa)-color(white)(aaaa)+

color(white)(aaaa)f(m)color(white)(aaaaaa)-color(white)(aaaa)+color(white)(aaaa)-color(white)(aaaa)+

Therefore,

f(m)>0, when m in ]-3,0 [uu]5, +oo[