If `alpha,beta` are real and distinct roots of `a x^2+b x-c=0a n dp ,q` are real and distinct roots of `a x^2+b x-|c|=0,w h e r e(a >0),` then (a)`alpha,beta in (p ,q)` (b). `alpha,beta in [p ,q]` (c). `p ,q in (alpha,beta)` (d). none of these

If alpha beta( alpha lt beta) are two distinct roots of the equation. ax^(2)+bx+c=0 , then

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 =

Let alpha and beta be the real and distinct roots of the equation ax^2+bx+c=|c|,(agt0) and p,q be the real and distinct roots of the equation ax^2+bx+c=0. Then which of the following is true? (A) p and q lie between alpha and beta (B) p and q lies outside (alpha, beta) (C) only p lies between alpha and beta (D) only q lies between (alpha and beta)

If alpha and beta are non-real, then condition for x^(2) + alpha x + beta = 0 to have real roots, is

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

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0t h e nh= -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/q-q/p) d. none of these

If alpha, beta in C are distinct roots of the equation x^2+1=0 then alpha^(101)+beta^(107) is equal to

If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^2 are the roots of a^2x^2+b^2x+c^2=0 , then a ,b ,c are in (A) G.P. (B) H.P. (C) A.P. (D) none of these

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