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 n h=` a. `-1/2(a/b-p/q)` b. `(b/a-q/p)` c. `1/2(b/a-q/p)` d. none of these

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 the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^2)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)

If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n di f(alpha//beta),(beta//alpha) are the roots of x^n+1+(x+1)^n=0,t h e nn( in N) a. must be an odd integer b. may be any integer c. must be an even integer d. cannot say anything

IF alpha,beta be the roots of the equation x^2+px+q=0 , show that 1/(alpha+beta) and 1/alpha+1/beta are the roots of pqx^2+(p^2+q)x+p=0

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

If sec alpha and "cosec" alpha are the roots of x^(2)- px+q=0 then show that p^(2)=q(q+2)

If alpha,beta are real and distinct roots of a x^2+b x-c=0 and p ,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