Answer :
Final answer:
The rational zeros of the polynomial P(x)=x⁴-x³-23x²-3x+90 are -1, -2, 3, and 5, which is determined by applying the Rational Root Theorem.
Explanation:
To find the rational zeros of a polynomial, we first need to apply Rational Root Theorem. This theorem states that if p/q is a zero (where p and q aren't zero), then p is a factor of the constant term, and q is a factor of the leading coefficient.
In the case of the polynomial P(x) = x⁴ - x³ - 23x² - 3x + 90, the constant term is 90 and the leading coefficient is 1. Factors of 90 are ±1, ±2, ±3, ±5, ±6, ±9, ±10, ±15, ±18, ±30, ±45, ±90. Since our leading coefficient is 1, the possible values are ±1. Therefore, checking these values in the polynomial, we find that the rational zeros (or roots) of P(x) are -1, -2, 3, and 5.
Learn more about Rational Zeros here:
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