Question

lambda^3 - 3lambda^2-18 + 0 = 0

If possible could someone show me how to find the roots of this equation, step by step, thanks.

Answer 1

does that really say +0= 0 at the end?

Answer 2

you can drop it off i guess

Answer 3

so you are solving
\[x^3-3x^2-18=0\] use a calculator because you are not going to do this by hand
http://www.wolframalpha.com/input/?i=x%5E3-3x%5E2-18%3D0

Answer 4

i understand the roots are lambda = -3 and lambda = 6 just not sure how to arrive at that answer with all working

Answer 5

need to show working it's for an assignment

Answer 6

then as you can see by the link i sent the equation is wrong or the solutions are wrong

Answer 7

now if the equation was
\[\lambda^2-3\lambda-18=0\] then the solutions would in fact be
\[\lambda = -3,\lambda =6\]

Answer 8

http://www.wolframalpha.com/input/?i=lambda%5E3+-3lambda%5E2-18lambda+%3D+0

Answer 9

yes thats correct, ow do you get -3 and 6

Answer 10

factor
\[(\lambda +3)(\lambda -6)=0\] etc

Answer 11

oooooooooooooooh you have a different equation!

Answer 12

you have
\[\lambda ^3 -3\lambda ^2-18\lambda =0\]

Answer 13

yep, i take a lambda outside to get your equation though cant i?

Answer 14

make a big difference. in that case you still factor as
\[\lambda(\lambda+3)(\lambda -6)=0\] and get three solutions. -3,0,6

your question was missing the last lambda

Answer 15

yes, i have it now thanks satelite73