Algebra-2

The Conjugate Root Theorem states that if a polynomial has rational coefficients and a complex number  is a root of the polynomial (where  and  are real numbers and ), then its complex conjugate  is also a root of the polynomial.

In this case, since the quartic polynomial  has rational coefficients and  is a root. According to the Conjugate Root Theorem,  must also be a root.

Now, for the root . If a polynomial with rational coefficients has a root of the form , then  is also a root. Here

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