How many real roots the equation possess

Question

$$e^x=m(m+1),\; m<0$$ I draw the graph of R.H.S and LHS and got it intersect at one point . But i dont know whether my procedure is right or wrong. Plz help me. The options are 1) no real root. 2) exactly one. 3) two real roots.

Answer 1

Plot the curves for some values of $m<0$, e.g. $m=-2$ or $m=-1/2$. What do you find?

Since $e^x$ is strictly increasing, there is at most one real solution. If there is a real solution then it is $x=\ln(m(m+1))$. Now you have to look for values of $m$ with $m(m+1) > 0$. I guess you can continue.