SOLUTION: The problem is= Determine all zeros for each polynomial function. P(X)= x3-4x2+x All I had was below x2(X-4)(x+1) one answer which is 0, but then I determined my factorin

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The problem is= Determine all zeros for each polynomial function. P(X)= x3-4x2+x All I had was below x2(X-4)(x+1) one answer which is 0, but then I determined my factorin      Log On


   

Question 106019: The problem is= Determine all zeros for each polynomial function.
P(X)= x3-4x2+x
All I had was below
x2(X-4)(x+1)
one answer which is 0, but then I determined my factoring was incorrect and I feel like the problem is missing something, should it have a zero on the end?
Please help.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
P%28X%29=+x3-4x2%2Bx
P%28x%29 = x*(x%5E2 – 4x + 1) this product will be equal to 0
if x=0 or (x%5E2 – 4x + 1) is equal to 0
So,
One zero will be for x=0
To find other two zeros, we need to solve
+x%5E2 – 4x + 1,
and find out for what value of x is equal to 0
+x%5E2 – 4x + 1 =+0

We can use square root formula:
x%281%2C2%29=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29

x%281%2C2%29=%28-%28-4%29+%2B-+sqrt+%28%28-4%29%5E2+-4%2A1%2A1+%29%29+%2F+%282%2A1%29
x%281%2C2%29=%284%2B-+sqrt+%2816+-4+%29%29+%2F+%282%29
x%281%2C2%29=%284%2B-+sqrt+%2812+%29%29+%2F+%282%29
x%281%2C2%29=%284%2B-+sqrt+%284%2A3+%29%29+%2F+%282%29
x%281%2C2%29=%284%2B-+2sqrt+%283+%29%29+%2F+%282%29
x%281%29=%284%2B+2sqrt+%283+%29%29+%2F+%282%29
x%281%2C2%29=2%282%2B+sqrt+%283+%29%29+%2F+%282%29 eliminate 2 in both nominator and denominator
x%281%29=2%2B+sqrt+%283+%29+
Use same way to find x2
x%282%29=2+-+sqrt+%283+%29+
the real zeros are: 0, 2%2B+sqrt%283%29, and 2+-+%28sqrt%283%29%29
since sqrt%283%29+=+1.73, we can write
2%2B+sqrt%283%29= 2+%2B+1.73=+3.73 and+ second zero
2- sqrt%283%29= 2+-+1.73= 0.27 third zero
so, the real zeros are: 0, 3.73, and+0.27