[" If "m,n,k" are rational and "m=k+(n)/(k)," then the "],[" roots of "x^(2)+mx+n=0" are "]

If mn,k are rational and m=k+(k)/(n) then the roots of x^(2)+mx+n=0 are

IF l,m,n are rational the roots of (m +n) x^2 -(l+m+n)x+l =0 are

If the roots of lx^(2)+2mx+n=0 are real and distinct then the roots of (l+n)(lx^(2)+2mx+n)=2(ln-m^(2))(x^(2)+1) will be

If x, y, k, m, n are positive and x + y = k, then find the maximum value of x^(m)y^(n) .

If L+M+N=0 and L,M,N are rationals the roots of the equation (M+N-L)x^(2)+(N+L-M)x+(L+M-N)=0 are

If x=1 and x=-3 as the roots of 3x^2+2mx+3n=0 ,then find m and n.

If m and n are roots of the equation (x+p)(x+q)-k=0 then find the roots of the equation (x-m)(x-n)+k=0

Prove that the integral values of m for which the roots of the equation mx^(2)+ (2m-1)x+(m-2)=0 are rational are given by the expression n(n+1) , where n is integer.

If the roots of the quadratic equation m x^(2) - n x + k = 0 are tan 33^(@) and tan 12^(@) , then the value of (2m + n + k)/(m) is equal to