Question

show that x^2+2x+3 has no zero

Answer 1

${x}^{2} + 2x + 3 = 0 \\ x = \frac{ - 2 + - \sqrt{4 - 12} }{2} \\ = \frac{ - 2 + - \sqrt{ - 8} }{2}$
here D<0
D=
${b}^{2} - 4ac$
if it is less then zero it indicates that given polynomial has no real roots.