The equation `(1/p-1/q)x^2+(2/q-2/r)x+(4/r-4/p)=0` has both most are real and equal then?

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 the roots of the equation x^(2)+(p+1)x+2q-q^(2)+3=0 are real and unequal AA p in R then find the minimum integral value of (q^(2)-2q)

If the roots of the equation (1-q+p^(2)/2)x^(2) + p(1+q)x+q(q-1) +p^(2)/2=0 are equal, then show that p^(2) = 4q

If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in A.P.

If the roots of the equation (1-q+(p^(2))/(2))x^(2)+p(1+q)x+q(q-1)+(p^(2))/(2)=0 are equal then show that p^(2)=4q