Answer
The minimum number of real zeros of a polynomial function is 1.
Work Step by Step
The Conjugate Pairs Theorem states that when a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. This means that, when $(p +i \ q)$ is a zero of a polynomial function with a real number of the coefficients, then its conjugate $(p –i q)$, is also a zero of the function.
We can notice that the function has a degree of $5$, so it has $5$ complex (including real) zeros.
Since, the conjugate zeros are in pairs, then there must be an even number of them. This means that the polynomial function can attain a maximum of $4$ complex roots.
Therefore, the minimum number of real zeros of the polynomial function is 1.
