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Given:
The function is:
To find:
All the possible rational zeros for the given function by using the Rational Zero Theorem.
Solution:
According to the rational root theorem, all the rational roots are of the form , where p is a factor of constant term and q is a factor of leading coefficient.
We have,
Here,
Constant term = -2
Leading coefficient = 10
Factors of -2 are ±1, ±2.
Factors of 10 are ±1, ±2, ±5, ±10.
Using the rational root theorem, all the possible rational roots are:
.
Therefore, all the possible rational roots of the given function are .