What is the polynomial of the smallest degree with integer coefficients and with zero's [3,1+i,-1]

If p(x) be a polynomial of the lowest degree with integer coefficients such that one of its roots is (sqrt(2)+3sqrt(3)) then |p(1)| is equal to

Obtain a polynomial of lowest degree with integral coefficient,whose one of the zeroes is sqrt(5)+sqrt(2)

Relationship between zeros of polynomial with degree >3 and its coefficients

Algorithm to factorize polynomials with integer coefficients (Step 1to Step 7)

If y is a polynomial of degree n in x and first coefficient is 2 then D^(n-1)(y)=

Find a quadratic polynomial whose zeros are 1 and -3 . Verify the relation between the coefficients and zeros of the polynomial.

Find the zeroes of the polynomial x^(2)+(1)/(6)x-2, and verify the relation between the coefficients and the zeroes of the above polynomial.

What is Real polynomial; complex polynomial ;degree of a polynomial?

Let f(x) be polynomial of degree 4 with roots 1,2,3,4 and leading coefficient 1 and g(x) be the polynomial of degree 4 with roots 1,1/2,1/3 and 1/4 with leading coefficient 1. Then lim_(xto1)(f(x))/(g(x)) equals

The least degree of a polynomial with integer coefficient whose one of the roots may be cos 12^(@) is