SOLUTION: factor the polynomial and use the factored form to find the zeros p(x)=x^4-3x^3+27x-81 x= please enter answers with a comma separated list.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the polynomial and use the factored form to find the zeros p(x)=x^4-3x^3+27x-81 x= please enter answers with a comma separated list.      Log On


   

Question 977233: factor the polynomial and use the factored form to find the zeros
p(x)=x^4-3x^3+27x-81
x=
please enter answers with a comma separated list.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x%5E4-3x%5E3%2B27x-81
f%28x%29=%28x%5E4-3x%5E3%29%2B%2827x-81%29
f%28x%29=x%5E3%28x-3%29%2B27%28x-3%29
f%28x%29=%28x-3%29%28x%5E3%2B27%29
f%28x%29=%28x-3%29%28x%2B3%29+%28x%5E2-3x%2B9%29
set f%28x%29=0
0=%28x-3%29%28x%2B3%29+%28x%5E2-3x%2B9%29
if 0=%28x-3%29=>x=3
if 0=%28x%2B3%29=>x=-3
if0=%28x%5E2-3x%2B9%29=>use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-3%29+%2B-+sqrt%28%28-3%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+

x+=+%283+%2B-+sqrt%289-36+%29%29%2F2+

x+=+%283+%2B-+sqrt%28-27+%29%29%2F2+
x+=+%283+%2B-+sqrt%28-9%2A3+%29%29%2F2+
x+=+%283+%2B-+3i%2Asqrt%283+%29%29%2F2+
x+=+%283%2F2%29%281+%2B-+3i%2Asqrt%283+%29%29+
x+=+%283%2F2%29+%281-i%2Asqrt%283%29%29 and x+=+%283%2F2%29+%281%2Bi%2Asqrt%283%29%29



so, zeros are:(x%5B1%5D,x%5B2%5D,x%5B3%5D,x%5B4%5D)=(3,-3,%283%2F2%29+%281-i%2Asqrt%283%29%29,%283%2F2%29+%281%2Bi%2Asqrt%283%29%29)