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`

Let p o* 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 .

If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then the largest value of m is psqrtq whre p, q are coprime natural numbers, then p +q=