Sum of roots of equations `f(x) - g(x)=0` is
(a)0 (b) `2alpha` (c) `-2alpha` (d) `4alpha`

Let alpha+iotabeta , alpha,betaepsilonR be a root of x^3+qx+r=0 If gamma be a real root of equation x^3+qx+r=0 then gamma (A) -2alpha (B) alpha (C) 2alpha (D) -alpha

If alpha, beta are the roots of the equations x^2+px+q=0 then one of the roots of the equation qx^2-(p^2-2q)x+q=0 is (A) 0 (B) 1 (C) alpha/beta (D) alpha beta

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

Let alpha,beta be the roots of the equation ax^2+bx+c=0 . A root of the equation a^3x^2+abcx+c^3=0 is (i) alpha+beta (ii) alpha^2+beta (iii) alpha^2-beta (iv) alpha^2beta

Let alpha,beta be the roots of the equation ax^2+bx+c=0 . A root of the equation a^3x^2+abcx+c^3=0 is (i) alpha+beta (ii) alpha^2+beta (iii) alpha^2-beta (iv) alpha^2beta

If sinx+cos e cx+tany+coty=4 where x a n d y in [0,pi/2],t h e ntan(y/2) is a root of the equation (a) alpha^2+2alpha+1=0 (b) 2 alpha^2-2alpha-1=0 (c) 2alpha^2-2alpha-1=0 (d) alpha^2-alpha-1=0

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

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

Let alpha be a root of the equation x ^(2) - x+1=0, and the matrix A=[{:(1,1,1),(1, alpha , alpha ^(2)), (1, alpha ^(2), alpha ^(4)):}] and matrix B= [{:(1,-1, -1),(1, alpha, - alpha ^(2)),(-1, -alpha ^(2), - alpha ^(4)):}] then the vlaue of |AB| is:

If alpha,beta are the roots of the equation x^(2)+px+q=0 , find the value of (a) alpha^(3)beta+alphabeta^(3) (b) alpha^(4)+alpha^(2)beta^(2)+beta^(4) .