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 - 6 Answer by lwsshak3(11628) (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
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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
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