If a and b are the roots of `x^2 – 3x + p = 0` and c, d are roots of `x^(2) – 12x + q = 0` , where a,b,c,d form a G.P Prove that (q+p):(q-p) = 17 : 15

If p and q are the roots of the equation x^(2)+px+q=0 , then

If 2 + isqrt3 is a root of x^(3) - 6x^(2) + px + q = 0 (where p and q are real) then p + q is

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 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 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 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 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 the roots of x^2+p x+q=0a n dgamma,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