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

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

If p and q are the roots of x^2 + px + q = 0 , then find p.

If a\ a n d\ b are roots of the equation x^2-p x+q=0 ,then write the value of 1/a+1/bdot

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

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

Let a, b are roots of equation x^2 - 3x + p = 0 and c, d are roots of equation x^2 - 12x + q = 0. If a, b, c, d (taken in that order) are in geometric progression then (q+p)/(q-p) is equal to (A) 5/7 (B) 15/17 (C) 17/15 (D) 7/5

If a,b are roots of x^2+px+q=0 and c,d are the roots x^2-px+r=0 then a^2+b^2+c^2+d^2 equals (A) p^2-q-r (B) p^2+q+r (C) p^2+q^2-r^2 (D) 2(p^2-q+r)

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P || B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q) .

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