Question

Find all constants λ ∈ R for which every nontrivial solution of the following
equation has at most one zero
y′′(x) + 10y′(x) + λy(x) = 0.

Answer 1

the way I'm figuring this, you will have at most one zero iff you have a double root

Answer 2

to the characteristic I mean

Answer 3

so lambda can only have one value