`alpha = sqrt2 ` and `beta = 1/3` so , find the polynomial = ?

If tan alpha = sqrt(3) and tan beta = (1)/(sqrt(3)) , then find the value of cot (alpha + beta) .

If alpha and beta are the zeroes of the polynomial x^(2)+4x+3=0 ,find the polynomial whose zeroes are 1+(beta)/(alpha) and 1+(alpha)/(beta)

If alpha and beta are the zeroes of the polynomial f(x) = 3x^(2)+5x+7 then find the value of (1)/(alpha^(2))+(1)/(beta^(2)) .

If alpha and beta are the zeros of the polynomial p(x) = x^(2) - px + q , then find the value of (1)/(alpha)+(1)/(beta)

If alpha and beta are the zeros of the polynomial f(x) = 4x^2 - 5x +1 , find a quadratic polynomial whose zeros are alpha^(2)/beta and beta^(2)/alpha

If alpha and beta be the zeros of the polynomial ax^(2)+bx+c, then the value of sqrt((alpha)/(beta))+sqrt((beta)/(alpha))

If alpha and beta are zeros of x^(2) - 2x + 3 , find a polynomial whose zeros are : i] alpha +2, beta + 2 ii] (alpha - 1)/( alpha + 1) , (beta - 1)/( beta + 1)

If alpha and beta are the zeroes of the polynomial ax^(2)+bx+c, find (i)alpha^(2)-beta^(2).(ii)alpha^(3)-beta^(3)

Find the value of 1/alpha + 1/beta if alpha and beta are the zeroes of the polynomial x^2 + x + 1.

If alpha and beta be the zeros of the polynomial x^(2)+x+1 , then find the value of (1)/(alpha)+(1)/(beta) .