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 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 ratios of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^)/(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+p x+q=0a n dgamma,delta are the roots of x^2+r x+s=0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p ,q ,r ,a n dsdot Deduce the condition that the equation has a common root.

If alpha,beta are the roots of the equation x^2+p x+q=0,t h e n-1/alpha,-1/beta are the roots of the equation (a) x^2-p x+q=0 (b) x^2+p x+q=0 (c) q x^2+p x+1=0 (d) q x^2-p x+1=0

If alpha,beta are the roots of x^2+p x+q=0 and gamma,delta are the roots of x^2+p x+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= (a) \ 1 (b) \ q (c) \ r (d) \ q+r

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

Let a, b, c, p, q be the real numbers. Suppose alpha,beta are the roots of the equation x^2+2px+ q=0 . and alpha,1/beta are the roots of the equation ax^2+2 bx+ c=0 , where beta !in {-1,0,1} . Statement I (p^2-q) (b^2-ac)>=0 Statement 11 b !in pa or c !in qa .

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

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)