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Find the roots of the polynomial $108x^4-75x^2+12$ by putting it in the form of an equation and then set it equal to zero
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$108x^4-75x^2+12=0$
Learn how to solve equations problems step by step online. Find the roots of 108x^4-75x^2+12. Find the roots of the polynomial 108x^4-75x^2+12 by putting it in the form of an equation and then set it equal to zero. Factor the polynomial 108x^4-75x^2+12 by it's greatest common factor (GCF): 3. We can factor the polynomial \left(36x^{3}+24x^{2}-9x-6\right) 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 -6. Next, list all divisors of the leading coefficient a_n, which equals 36.