Let p & q be the two roots of the equation, `mx^2+x(2-m)+3=0`. Let `m_1,m_2` be the two values of m satisfying `p/q+q/p=2/3` Determine the numerical value of `m_1/m_2^2+m_2/m_1^2`

If the product of roots of the equation mx^(2)+6x+(2m-1)=0 is -1 then the value of m is

If the roots of the equation lx^(2) +mx +m=0 are in the ratio p:q, then

If the quadratic equation mx^2+2x+m=0 has two equal roots, then the values of m are

If p and q are roots of the quadratic equation x^(2) + mx + m^(2) + a = 0 , then the value of p^(2) + q^(2) + pq , is

If p and q are roots of the quadratic equation x^(2) + mx + m^(2) + a = 0 , then the value of p^(2) + q^(2) + pq , is

If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be m:n, then prove that p^(2)mn=q(m+n)^(2) .

If the sum of the roots of the equation x^(2)-px+q=0 be m times their difference, prove that p^(2)(m^(2)-1)=4m^(2)q .

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and (alpha)/(2),2 beta be the roots of the equation x^(2)-qx+r=0, the value of r is (2007,3M)x^(2)-qx+r=0, the value of r is (2007,3M)(2)/(9)(p-q)(2q-p)(b)(2)/(9)(q-p(2p-q)(2)/(9)(q-2p)(2q-p)(d)(2)/(9)(2p-q)(2q-p)

If m=(4pq)/(p+q) , then the value of (m+2p)/(m-2p)+(m+2q)/(m-2q)