If the equation `x^2 + px + q =0` and `x^2 + p' x + q' =0` have common roots, show that it must be equal to `(pq' - p'q)/(q-q')` or `(q-q')/(p'-p)`.

If p,q,r are in G.P. and the equations, px^(2) + 2qx + r = 0 and dx^2+2ex + f = 0 have a common root, then show that d/p , e/q, f/r are in A.P.

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

If -4 is a root of the equation x^(2)+px-4=0 and if the equation x^(2)+px+q=0 are equal roots, find the values of p and q.

Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2beta be the roots of the equation x^2-q x+r=0. Then the value of r is 2/9(p-q)(2q-p) b. 2/9(q-p)(2q-p) c. 2/9(q-2p)(2q-p) d. 2/9(2p-q)(2q-p)

If the roots of the quadratic equation ax^(2) + cx + c = 0 are in the ratio P : q then show that sqrt (p/q) + sqrt (q/p) + sqrt (c/a) = 0

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

Consider quadratic equations x^2-ax+b=0 and x^2+px+q=0 If the above equations have one common root and the other roots are reciprocals of each other, then (q-b)^2 equals

Show that ( p ^^ q) to (p vv q) is a tautology.