The equation `Px^(2) + qx + r = 0 ` (where p, q, r, all are positive ) has distinct real roots a and b .

If x^(2) - px + q = 0 (p,q in R and p ne 0, q ne 0) has distinct real roots. Then…

If the roots of the equation px ^(2) +qx + r=0, where 2p , q, 2r are in G.P, are of the form alpha ^(2), 4 alpha-4. Then the value of 2p + 4q+7r is :

If the roots of the equation px ^(2) +qx + r=0, where 2p , q, 2r are in G.P, are of the form alpha ^(2), 4 alpha-4. Then the value of 2p + 4q+7r is :

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

Let alpha and beta be the roots of the equation px^(2) + qx + r=0 . If p, q, r in AP and alpha+beta =4 , then alpha beta is equal to

If the roots of the equation qx^2 + 2px + 2q =.0 are real and unequal then prove that the roots of the equation (p + q)x^2 + 2qx + (p - q)=0 are imaginary,