Answer :
Final answer:
To find the real zeros of a function, we can use the Rational Zero Theorem. By testing the possible rational zeros obtained from the theorem, using synthetic division or long division, we can determine the real zeros of the function f(x)=2x^(4)-23x^(3)+94x^(2)-157x+84. The real zeros of this function are 1, 2, 3, and 7.
Explanation:
To find the real zeros of the function f(x)=2x^(4)-23x^(3)+94x^(2)-157x+84, we can use the Rational Zero Theorem. According to the theorem, the possible rational zeros of a polynomial function are found by taking the factors of the constant term (in this case, 84) and dividing them by the factors of the leading coefficient (in this case, 2). By testing these possible zeros using synthetic division or long division, we can find the real zeros of the function.
For this function, the possible rational zeros are ± 1, ± 2, ± 3, ± 4, ± 6, ± 7, ± 12, ± 14, ± 21, ± 28, ± 42, ± 84. By testing these possible zeros using synthetic division, we find that the real zeros of the function are 1, 2, 3, and 7.
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