Show that the roots of the equation x2-2(m+1/m)x+3=0 are real for all(non zero)real values of m - Maths - Complex Numbers and Quadratic Equations

Question

Show that the roots of the equation x2-2(m+1/m)x+3=0 are
real for all(non zero)real values of m ?

Manbar Singh · Accepted Answer

x2 - 2m + 1mx + 4 = 0Now, a = 1; b = -2m + 1m; c = 4Now, D = b2-4ac = 4m+1m2 - 16=4m2 + 1m2 + 2 - 16= 4m2 + 4m2 + 8 - 16=4m2 + 4m2 - 8=4m2 + 1m2 - 2=4m - 1m2Now, D = 4m - 1m2 >0So, the roots of the given equation are real

Show that the roots of the equation x2-2(m+1/m)x+3=0 are real for all(non zero)real values of m....?

Show that the roots of the equation x²-2(m+1/m)x+3=0 are real for all(non zero)real values of m....?