Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots and square root 5 and 2?

We are asked in the problem to determine the polynomial function with a leading coeffiient of 3 and whose roots are square root of 5 and 2. In this case, the poolynomial function becomes:

(x-√5) (x-2) = x^2 - 2(2+√5) + 2√5
since the leading coefficient is 3, then the answer becomes
(x^2 - 2(2+√5) + 2√5)*3 = 3x^2 - 6(2+√5) + 6√5
 

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