f(x)=x^3-3x^2+4 find the zeros? I know what the answer is, I just don't know how to get it...could you explain in detail please?? and what is a duplicate root?

Question

amistre64 · Answer

factor, trial and error, etc.

a duplicate root might suggest that the factored form has 2 of the same factors

amistre64 · Answer

a rational roots method might bring about something close; and narrow down any trial and error

amistre64 · Answer

$$\pm\frac{factors.of.last}{factors.of.first}$$

amistre64 · Answer

since the first number is 1; it makes life alot easier :)

amistre64 · Answer

so factors of 4 are:  1,2,4  plus or minus of course

amistre64 · Answer

lets see if any of these makes a zero ..

f(x) = x^3-3x^2+4

f(1)=1-3+4 = not 0
f(-1)=-1-3+4 = 0 ... -1 is a root
f(2) = 8-12+4 = 0 ... 2 is a root
f(-2) = -8-12+4 = not 0
f(4) = 64-48+4 = not 0
f(-4) = -64-48+4 = not 0

amistre64 · Answer

so we know that (x+1)(x-2) can be divided out of it: and that we are missing another root, since its a 3degree poly.  That means that one of these most likely is duplicated

amistre64 · Answer

logic would says its the (x-2)

anonymous · Answer

thanks!! I get it now. :DD