If `alpha,beta` are the roots of the equation `a x^2+b x+c=0,` then find the roots of the equation `a x^2-b x(x-1)+c(x-1)^2=0` in term of `alphaa n dbetadot`

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are

If alphaa n dbeta are roots of the equation a x^2+b x+c=0, then the roots of the equation a(2x+1)^2-b(2x+1)(x-3)+c(x-3)^2=0 are a. (2alpha+1)/(alpha-3),(2beta+1)/(beta-3) b. (3alpha+1)/(alpha-2),(3beta+1)/(beta-2) c. (2alpha-1)/(alpha-2),(2beta+1)/(beta-2) d. none of these

Let a ,b ,c be real numbers with a!=0a n dl e talpha,beta be the roots of the equation a x^2+b x+c=0. Express the roots of a^3x^2+a b c x+c^3=0 in terms of alpha,betadot

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

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

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

Let a, b, c be real numbers with a = 0 and let alpha,beta be the roots of the equation ax^2 + bx + C = 0 . Express the roots of a^3x^2 + abcx + c^3 = 0 in terms of alpha,beta

If alpha, beta are the roots of the equation x^(2)+x+1=0 , then the equation whose roots are alpha^(22)" and "beta^(19) , is

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot