If `p, q, r, s in R`, then equaton `(x^2 + px + 3q) (-x^2 + rx + q) (-x^2 + sx-2q) = 0` has

If every pair from among the equations x^ 2 + p x + q r = 0, x^2+px+qr=0, x^2 + q x + r p = 0, x^2+qx+rp=0 and x^2 + r x + p q = 0, x^2+rx+pq=0 has a common root then the product of three common root is (A) pqr (B) 2pqr (C) (p^2q^2r^2) (D)none of these

If alpha, beta are the real roots of x^(2) + px + q= 0 and alpha^(4), beta^(4) are the roots of x^(2) - rx + s = 0 , then the equation x^(2) - 4 q x + 2q^(2) - r = 0 has always

If -3 is a root of the equation x^2+ px + 6 = 0 and the equation x^2 +px +q = 0 has equal roots, find p,q .

If p, q, r are the roots of the equation x^3 -3x^2 + 3x = 0 , then the value of |[qr-p^2, r^2 , q^2],[r^2,pr-q^2,p^2],[q^2,p^2,pq-r^2]|=

For p,q in R, the roots of (p^2+q^2)x^2+2(p+q)x+2=0 are

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 the roots of the equation q^2 x^2 + p^2 x + r^2 =0 are the squares of the roots of the equation qx^2 + px + r=0 , then p,q,r are in ………………….. .

p, q, r and s are integers. If the A.M. of the roots of x^(2) - px + q^(2) = 0 and G.M. of the roots of x^(2) - rx + s^(2) = 0 are equal, then