Form the values of `(1)/(alpha^(2))+(1)/(beta^(2))` in terms of a, b, c if `alpha, beta` are roots of `ax^(2)+bx+c=0`, `c != 0`

Form the values of (1)/(alpha)+(1)/(beta) in terms of a, b, c if alpha, beta are roots of ax^(2)+bx+c=0 , c != 0

Find the values of alpha^(3)+beta^(3) in terms of a, b, c if alpha, beta are roots of ax^(2)+bx+c=0 , c != 0

If alpha. beta are the roots of x^2 +bx+c=0 and alpha + h, beta + h are the roots of x^2 + qx +r=0 then 2h=

If alpha, beta are the roots of x^(2) + bx + c = 0 and, alpha +h, beta+h are the roots of x^(2) + qx +r = 0 then h =

If 0 gt a gt b gt c and the roots alpha, beta are imaginary roots of ax^(2) + bx + c = 0 then

If alpha, beta are the roots of ax^(2) + bx + c = 0 and alpha + h, beta + h are the roots of px^(2) + qx + r = 0 , then h =

Assertion (A) : If alpha, beta are the roots of ax^(2) + bx + c = 0 then the equation whose roots are (alpha-1)/(alpha), (beta-1)/(beta) is c(1-x)^(2)+ b(1-x)+a=0 Reason (R): If alpha, beta are the roots of f(x) = 0 then the equation whose roots are (alpha-1)/(alpha) and (beta-1)/(beta) is f((1)/(1-x))=0

In the quadratic equation ax^2 + bx + c = 0 , if Delta = b^2-4ac and alpha + beta, alpha^2 + beta^2, alpha^3 + beta^3 are in GP. where alpha, beta are the roots of ax^2 + bx + c =0 , then

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

If alpha , beta are the roots of x^2-p(x+1)+c=0 then (1+alpha )( 1+ beta )=