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

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

If p, q, r each are positive rational number such tlaht p gt q gt r and the quadratic equation (p + q - 2r)x^(2) + (q + r- 2p)x + (r + p - 2q) = 0 has a root in (-1 , 0) then which of the following statement hold good? (A) (r + p)/(q) lt 2 (B) Both roots of given quadratic are rational (C) The equation px^(2) + 2qx + r = 0 has real and distinct roots (D) The equation px^(2) + 2qx + r = 0 has no real roots

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 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]|=

If alpha,beta are roots of the equation (3x+2)^(2)+p(3x+2)+q=0 then roots of x^(2)+px+q=0 are