Let `a=cos 1^(@)` and `b= sin 1^(@)`. We say that a real number is algebraic if is a root of a polynomial with integer coefficients. Then

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

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

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

Let u, v be two real numbers such that u,v and uv are roots of a cubic polynomial with rational coefficients. Prove or disprove uv is rational.

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

Let a,b be integers and f(x) be a polynomial with integer coefficients such that f(b)-f(a)=1. Then, the value of b-a, is

Let a,b be integers and f(x) be a polynomial with integer coefficients such that f(b)-f(a)=1. Then, the value of b-a, is

The number of real roots of the polynomial equation x^(4)-x^(2)+2x-1=0 is

For any two real number a and b ,we define a R b if and only if sin^2a + cos^2b = 1 . The relation R is

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