Solve by factorization: `m/n x^2+n/m=1-2x`

Solve for x and y : mx- ny = m^(2) + n^(2) " " x - y = 2n

If m, n be natural numbers and (x^(2)-n) be a factor of the polynomial (ax^(2m)+bx^(2m+1)-1) , then prove that a=(1/n)^(m)andb=0 .

Solve the following system of equations by method of cross-multiplication: m x-n y=m^2+n^2,\ \ \ \ x+y=2m

If x-2 and x-1/2 both are the factors of the polynomial nx^2-5x+m , then show that m+n+2.

If x-2 and x-1/2 both are the factors of the polynomial nx^2 -5x+m , then show that m=n=2.

Solve The equation x^(2)+(2m+1)x+(2n+1)=0

Find the values of m and n, if (x-m) and (x-n) are the factors of the expression x^(2)+mx-n

Prove : int sin mx sin n x dx[ m^(2) != n^(2)] , = 1/2 [ (sin(m-n)x)/(m-n) - (sin (m+n)x)/(m+n) ] + c

if x+a is a factor of the polynomials x^(2)+px+q and x^(2)+mx+n prove that a=(n-q)/(m-p)

Prove that x^(m)+1 is a factor of x^(mn) - 1 if n is even.