Let `pa n dq` be the roots of the equation `x^2-2x+A=0` and let `ra n ds` be the roots of the equation `x^2-18 x+B=0.` If `p< q< r< s` are in arithmetic progression, then `A=` and `B=...` (1997, 2M)

The roots of the equation x^2+ax+b=0 are

Let alpha and beta be roots of the equation X^(2)-2x+A=0 and let gamma and delta be the roots of the equation X^(2)-18x+B=0 . If alpha lt beta lt gamma lt delta are in arithmetic progression then find the valus of A and B.

Let a, b be the roots of the equation x^(2) - 4 x +k_(1) = 0 and c , d the roots of the equation x^(2) - 36 x + k_(2) = 0 If a lt b lt c lt d and a, b,c,d are in G.P. then the product k_(1) k_(2) equals

Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2p is one of the roots of the equation

The roots of the equation x^(3) -2x^(2) -x +2 =0 are

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0a n dalpha^2,beta is the roots of quadratic equation x^2-q x+8=0 , then the value of rifr/8 is the arithmetic mean of p a n d q , is

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

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

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot