If `(alpha, beta)` be the circumcentre of the triangle whose sides are `3x-y=5, x+3y=4 and 5x+3y+1=0`, then (A) `11alpha - 21beta = 0` (B) `11alpha + 21beta = 0` (C) `alpha +2beta=0` (D) none of these

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

The image of the point A (1,2) by the line mirror y=x is the point B and the image of B by the line mirror y=0 is the point (alpha,beta) , then a. alpha=1,beta=-2 b. alpha = 0,beta=0 c. alpha=2,beta=-1 d. none of these

If alpha an integer and P (alpha, alpha^2) is a point in the interior of the quadrilateral x=0, y=0, 4x+y-21=0 and 3x+y-4=0, and (1+ax)^n = 1 + 8x+24x^2 + …, then alpha= (A) a (B) -a (C) a^2 (D) none of these

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

If alpha, beta are the roots of x^(2)+x+1=0 , then the equation whose roots are alpha^(5), beta^(5) is

If alpha, beta are roots of the equation ax^2 + bx + c = 0 then the equation whose roots are 2alpha + 3beta and 3alpha + 2beta is

If alpha and beta ( alpha'<'beta') are the roots of the equation x^2+b x+c=0, where c<0

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

If alpha , beta , gamma are the roots of x^3 -3x +1=0 then the equation whose roots are alpha - (1)/( beta gamma) , beta - (1)/( gamma alpha ) , gamma - (1)/( alpha beta ) is

the lines x + y + 1 = 0; 4x + 3y + 4 = 0 and x + alphay + beta= 0, where alpha^2 + beta^2 = 2, are concurrent