Answer :
Final answer:
The rational roots of the polynomial 4x^5-23x^4+7x-6 are x = 1 and x = -3.
Explanation:
The given polynomial is 4x5-23x4+7x-6. In order to find the rational roots of a polynomial, we can use the Rational Root Theorem. According to this theorem, if a rational number p/q is a root of the polynomial, then p must be a factor of the constant term (in this case, -6) and q must be a factor of the leading coefficient (in this case, 4).
So, the possible rational roots of the polynomial are: ±1, ±2, ±3, ±6. We can now try these values one by one in the polynomial and check for which values the polynomial equals to zero. By substituting these values into the polynomial, we find that the rational roots are: x = 1 and x = -3.
Therefore, the rational roots of the polynomial 4x5-23x4+7x-6 are x = 1 and x = -3.
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