If `px^(2) + qx + r = p ( x-a) ( x-B),and p^(3) + pq + r = 0 ,` p,q and r being real numbers, then which of the following is not possible?

Consider the cubic equation x^(3)+px^(2)+qx+r=0, where p,q, are real numbers,which of the following statement is correct?

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 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 p,q,r be the numbers in A.P.then roots of the equationp x^(2)+qx+r=0 are of

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

Prove that px^(q - r) + qx^(r - p) + rx^(p - q) gt p + q + r where p,q,r are distinct number and x gt 0, x =! 1 .

If px^(3)+qx^(2)+rx+s is exactly divisible by x^(2)-1 , then which of the following is /are necessarily true ? (A) p = r )B) q = s (C ) p =- r (D) q =- s