The number of all polynomial whose coefficients are all 1 , that have only real roots are

Step-by-step solution

If a polynomial a₀ x^n+a₁ x^ n-1 + . .+a_n is such a polynomial, We can assume a₀=1 , let r₁, r₂, . ., r_n are its roots r₁^2+r₂^2+ . .+r_n^2=a₁^2-2 a₂, r₁^2 r₂^2 . . r_n^2=a_n^2 A M G M a₁^2-2 a₂ n (a_n )^ 2 / n a₁, a₂= 1 , we must have a₂=-1 , and n 3 Polynomials are (x-1), (x+1), (x^2+x-1 ), (x^2-x-1 ), (x^3+x^2-x-1 ), (x^3-x^2-x+1 )