SOLUTION: list all possible zeros of y=3x^3-5x^2+4x-2

Algebra ->  Rational-functions -> SOLUTION: list all possible zeros of y=3x^3-5x^2+4x-2      Log On


   

Question 320347: list all possible zeros of y=3x^3-5x^2+4x-2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C300%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E3-5x%5E2%2B4x-2%29+
Looks like x=1 is a root.
Verify using the equation.
+y=3x%5E3-5x%5E2%2B4x-2
+y=3%2A1-5%2A1%2B4%2A1-2
+y=0
Use polynomial long division to find the remaining quadratic equation and then its roots.
.
.
.
First term: +highlight%28+3x%5E2+%29
3x%5E2%28x-1%29=3x%5E3-3x%5E2
Subtract from the original polynomial to get the remainder.
%283x%5E3-5x%5E2%2B4x-2%29-%283x%5E3-3x%5E2%29=-2x%5E2%2B4x-2
.
.
.
Second term: highlight%28+-2x%29
-2x%28x-1%29=-2x%5E2%2B2x
Subtract from the remainder to get the new remainder.
%28-2x%5E2%2B4x-2%29-%28-2x%5E2%2B2x%29=2x-2
.
.
.
Final term: highlight%28+2%29
2%28x-1%29=2x-2
Subtract from the remainder to get the new remainder.
%282x-2%29-%282x-2%29=0
.
.
.
%283x%5E3-5x%5E2%2B4x-2%29%2F%28x-1%29=3x%5E2-2x%2B2
Use the quadratic formula to get the roots of the quadratic equation.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+
x+=+%282+%2B-+sqrt%28+4-24+%29%29%2F%286%29+
x+=+%282+%2B-+sqrt%28+-20+%29%29%2F%286%29+
x+=+%282+%2B-+2sqrt%28+5+%29i%29%2F%286%29+
x+=+%281+%2B-+sqrt%28+5+%29i%29%2F3+