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 are the roots of x^(2)-ax+b^(2)=0 , then alpha^(2)+beta^(2) is equal to

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=0then 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 a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A.P. b. G.P. c. H.P. d. none of these

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 cos2B=(cos(A+C))/("cos"(A-C)) , then tanA ,t a n B ,tanC are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If alpha and beta are the roots of 2x^2-3x+7=0 , form the equations where roots are alpha^2+2 and beta^2+2 .

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

If a , b ,a n dc are in G.P., then a+b ,2b ,a n db+c are in a. A.P b. G.P. c. H.P. d. none of these

If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,beta+delta are the roots of A x^2+B x+C=0,(A!=0) for some constant delta then prove that (b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)