# SOLUTION: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 4x3 - 21x2 + 29x - 6

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 4x3 - 21x2 + 29x - 6      Log On

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 Click here to see ALL problems on Exponential-and-logarithmic-functions Question 470435: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 4x3 - 21x2 + 29x - 6Answer by lwsshak3(6456)   (Show Source): You can put this solution on YOUR website!Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 4x3 - 21x2 + 29x - 6 ** f(x) = 4x^3 - 21x^2 + 29x - 6 If you are allowed to use a graphing calculator, you will find that one of the zeros is 2. Using long division or synthetic division we can find the other two zeros. I will use synthetic division as follows: 2)......4......-21......29.......-6 ...................8......-26.........6 .........4.....-13.......3...........0 f(x)=(x-2)(4x^2-13x+3) f(x)=(x-2)(4x-1)(x-3) Ans: zeros are: 1/4, 2, and 3 see graph below as a visual check on answers ..