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Find the roots of the polynomial $\frac{12x^3+13x^2-59x+30}{4x-5}$ by putting it in the form of an equation and then set it equal to zero
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$\frac{12x^3+13x^2-59x+30}{4x-5}=0$
Learn how to solve equations problems step by step online. Find the roots of (12x^3+13x^2-59x+30)/(4x-5). Find the roots of the polynomial \frac{12x^3+13x^2-59x+30}{4x-5} by putting it in the form of an equation and then set it equal to zero. We can factor the polynomial 12x^3+13x^2-59x+30 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 30. Next, list all divisors of the leading coefficient a_n, which equals 12. The possible roots \pm\frac{p}{q} of the polynomial 12x^3+13x^2-59x+30 will then be.