Given that `(1+x)^6 (1+mx)^5 = 1+nx +415x^2 +...+m^5 x^11,` find the possible values of `m and n.`

If the polynomial f(x) = 2x^3 + mx^2 + nx - 14 has (x - 1) and (x + 2) as its factors, find the value of m x n.

(2)/(3) and 1 are the solutions of equation mx^(2)+nx+6=0 . Find the values of m and n.

If (x-3) is a factor of p(x)=x^(3)-mx^(2)+(m+1)x-12 find the value of 'm'

Given that x + (1//x) = 15 , then find the value of 5x ÷ (5x^(2) - 11 x + 5)

if (x+2) and (x-1) are the factors of (x^(3)+10x^(2)+mx+n), then the values of m and n are:-

If the function y = m log x + nx^(2) +x has its critcal points at x = -1 and x =2 then the values of m and n respectively are

If x is nearly equal to 1 then find the value of (mx^m - nx^n)/(m- n)

If ( x - 1 ) is the factor of the polynomial ( x^3 - 2x^2 + mx - 4 ) then find the value of m .