If roots of `2(x-a)(x+b)+c=0` are `alpha` and `beta` roots of `(x-alpha)(x-beta)-c/2=0` are `lamda a` an `mu b`, then `1/(lamda +mu)` is (where a and b are non zero real numbers)

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are

Let alpha,beta be the roots of the equation (x-a)(x-b)=c ,c!=0 Then the roots of the equation (x-alpha)(x-beta)+c=0 are

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

ax^2 + bx + c = 0(a > 0), has two roots alpha and beta such alpha 2, then

Let alpha and beta be the roots of x^2-x+p=0 and gamma and delta be the root of x^2-4x+q=0. If alpha,beta,a n dgamma,delta are in G.P., then the integral values of p and q , respectively, are

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

Let alpha,beta,gamma be the roots of (x-a) (x-b) (x-c) = d, d != 0 , then the roots of the equation (x-alpha)(x-beta)(x-gamma) + d =0 are :

Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if a_n=alpha^n-beta^n for n>=1 then the value of (a_10 - 2a_8)/(2a_9)

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

Suppose alpha, beta are roots of ax^(2)+bx+c=0 and gamma, delta are roots of Ax^(2)+Bx+C=0 . If alpha,beta,gamma,delta are in AP, then common difference of AP is