Let `alpha` and `beta` are real roots of the equation `3x^2 - (a^2 - 1)x + a^2 - 3a + 2 = 0` such that `log_alpha < 0`.If the range of a is `(m, oo)` find m.

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha and beta are the roots of the equation 2x^(2) - 3x + 4 = 0 , then alpha^(2) + beta^(2) = ____

Let alpha and beta be two real roots of the equation 5 cot ^(2) x- 3 cot x-1=0, then cot ^(2)(alpha + beta)=

Let alpha and beta be two real roots of the equation 5cot^2x-3cotx-1=0 , then cot^2 (alpha+beta) =

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , find the value of (i) (alpha)/(beta) + (beta)/(alpha) (ii) alpha-beta (iii) (alpha^(2))/(beta) + (beta^(2))/(alpha)

If alpha amd beta are the roots of the equation 3x^(2) - 2x - 8 = 0 then alpha^(2) + alpha beta + beta^(2) = "_____" .

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