One root of the quadratic equation `sin^2 theta x^2 - x + cos^2theta = 0` is given by

If alpha,beta are the roots of the quadratic equation x^2-2(1-sin2theta)x-2 cos^2(2theta) = 0 , then the minimum value of (alpha^2+beta^2) is equal to

Let alpha and beta be the roots of the quadratic equation x sin^(2) theta -x (sin theta cos theta + 1) + cos theta =0 (0le thetale 45^(@)) and alpha le beta . Then sum_(n=0)^(oo) (alpha^(n)+((-1)^(n))/(beta^(n))) is to equal to

If alpha,beta are the roots of the quadratic equation x^(2)-2(1-sin2 theta)x-2cos^(2)(2 theta)=0, then the minimum value of (alpha^(2)+beta^(2)) is equal to

If alpha,beta are the roots of the quadratic equation x^(2)-2(1-sin2 theta)x-2cos^(2)(2 theta)=0, then the minimum value of (alpha^(2)+beta^(2)) is equal to

Let alpha and beta be the roots of the quadratic equation x^(2) sin theta - x (sin theta cos theta + 1) + cos theta = 0 (0 lt theta lt 45^(@)) , and alpha lt beta . Then Sigma_(n=0)^(oo) (alpha^(n) + ((-1)^(n))/(beta^(n))) is equal to

Let alpha and beta be the roots of the quadratic equation x^(2) sin theta - x (sin theta cos theta + 1) + cos theta = 0 (0 lt theta lt 45^(@)) , and alpha lt beta . Then Sigma_(n=0)^(oo) (alpha^(n) + ((-1)^(n))/(beta^(n))) is equal to

Let alpha and beta be the roots of the quadratic equation x^(2) sin theta - x (sin theta cos theta + 1) + cos theta = 0 (0 lt theta lt 45^(@)) , and alpha lt beta . Then Sigma_(n=0)^(oo) (alpha^(n) + ((-1)^(n))/(beta^(n))) is equal to

If alpha, beta are the roots of the quadratic equation x^(2)-2(1-sin 2theta) x-2 cos^(2) 2 theta=0, (theta in R) then find the minimum value of (alpha^(2)+beta^(2)) .