If n is a root of the equation x^2+p x+m=0 and m is a root of the equation x^2+p x+n=0 , where m n , then what is the value of p+m+n ?

Step-by-step solution

Given, n is a root of x^2+p x+m=0 n ^2+ pn + m =0 ..(i) Given, m is a root of the equation x ^2+ px + n =0 m ^2+ pm + n =0 ...(ii) Now subtracting Eq (ii) from Eq (i), we get aligned & ( n ^2- m ^2 )+ p ( n - m )-( n - m )=0 & ( n - m )[( n + m )+ p -1]=0 & n + m + p -1=0 given, n m & n + m + p =1 aligned