SOLUTION: identify all rational zeros of the polynomial function f(x)=3x^4-5x^3-29x^2+45x+18

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Question 314766: identify all rational zeros of the polynomial function f(x)=3x^4-5x^3-29x^2+45x+18
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+-10%2C+10%2C+3x%5E4-5x%5E3-29x%5E2%2B45x%2B18%29+
Looks like zeros ar x=-3,2,3
Verify using the polynomial,
+3%28-3%29%5E4-5%28-3%29%5E3-29%28-3%29%5E2%2B45%28-3%29%2B18=243%2B135-261-135%2B18=0+
3%282%29%5E4-5%282%29%5E3-29%282%29%5E2%2B45%282%29%2B18=48-40-116%2B90%2B18=0
3%283%29%5E4-5%283%29%5E3-29%283%29%5E2%2B45%283%29%2B18=243-135-261%2B135%2B18=0
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+graph%28+300%2C300%2C+-2%2C+1%2C+-10%2C+10%2C+3x%5E4-5x%5E3-29x%5E2%2B45x%2B18%29+
A closer look reveal x=-1/3 as a possible root.

The four roots are then x=-3,-1%2F3,2,3