need help with these calculus problem?

Question

find the value of K such that y = e^(kx) is a solution of equation y''-8y'+15y=0
there should be two answrs :k1<=k2
need help asap
it would be nice if someone can explain it to me how they come up the answer. thanks

Answer 1

find y' and y''
plug in them in dif equation.

then find k

y'=k e^(kx)
y''=k^2 . e^(kx)

take out e^(kx) in the equation.

it can not be zero

k^2-8k+1=0

find k values from this equation
you will see them as k1