Question

x^2+1 has no real zeros why

Answer 1

${x}^{2} + 1 = 0 \\ {x}^{2} = - 1 \\ \sqrt{ {x}^{2} } \: = \sqrt{ - 1} \\ x = \sqrt{ - 1 } \\ x \: = i$
here x is not a real number , its an imaginary number...We cannot reperesent x on Real number line so the given expression will not have Real zero...To represent such zeros on Complex plane as i is a complex number...