Question

May someone please show me step by step how to solve this?
What are all the real zeros of y = (x - 12)3 - 10?

Answer 1

\[y = (x-12)^3-10\]

Answer 2

is that what you mean?

Answer 3

Yes... sorries.

Answer 4

there are no integer roots

Answer 5

I don't know what you mean..

Answer 6

well, 10 - 10 = 0, so that is one way to get a root:

0 = (x-12)^3 - 10, get rid of the 12 and add in cbrt(10)

0 = ((cbrt(10)+12)-12)^3 - 10

0 = (cbrt(10)+(12-12))^3 - 10

0 = (cbrt(10))^3 - 10

0 = 10 - 10

knowing 1 root, you can divide it out and reduce the setup to a quadratic

Answer 7

we can investigate the derivative as well to find the "humps" of the quadratic. if the zeros of the derivative produce the same sign in f(x) then we know they are on the same side of the x axis.



if the humps are on the same side of the x axis, then we can be assured that it only has 1 real root