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Answer :
The all possible rational zeros of f(x)=x⁶-2x⁴+7x²+25 are ±1, ±5 and ±25.
To find the possible rational zeros of the polynomial function f(x)=x⁶-2x⁴+7x²+25, we can use the Rational Root Theorem.
- The Rational Root Theorem states that any rational solution of a polynomial equation, expressed as a fraction p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.
- For the polynomial f(x), the constant term is 25, and the leading coefficient (coefficient of x⁶) is 1. Therefore, the factors of the constant term 25 are ±1, ±5, ±25, and the factors of the leading coefficient 1 are ±1.
- Thus, the possible rational zeros are: ±1, ±5 and ±25.
This gives us a total of six possible rational zeros: +1, -1, +5, -5, +25, -25.
However, it's important to note that these are just the possible rational zeros. These values should be tested in the function to determine if they are actual zeros.
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