If both roots of quadratic equation `(alpha+1)x^2-21 -(1+ 3alpha)x + 1 +8alpha= 0` are real and distinct then `alpha` be

If the roots of the quadratic equation 5x^2 - 2x - 3 = 0 be alpha and beta , find the value of (1)/(alpha)+(1)/(beta) .

Let alpha and beta are two distinct real roots of the quadratic equation (2a-1)x^(2)+x-1=0 . If alpha<2 < beta then a cannot take the value

If alpha and beta are the roots of quadratic equation x^2+5x-1=0 then, find alpha^3+beta^3

IF the roots of the equation 3x^2+8x+2=0 are alpha,beta then (1/alpha+1/beta) =

If alpha and beta are the roots of quadratic equation x^2+5x-1=0 then, find alpha^2+beta^2

IF alpha is a root of the equation 4x ^2 +2x-1=0 then 4 alpha ^3 - 3 alpha is

IF one root of the quadratic equation x^2-x-1=0 is alpha , prove that its other root is alpha^3-3alpha .

IF alpha be a root of the quadratic equation 4x^2+2x-1=0 , Let prove that 4alpha^3-3alpha is the other root.