Question

By using the method of completing the square show that ${4x}^2+3x+5=0$ has no real roots.

Answer 1

$x^2+3x+5=0$

$x^2+\frac{3}{4}x+\frac{5}{4}=0$

$x^2+\frac{3}{4}x+{\left(\frac{3}{8}\right)}^2=\frac{-5}{4}+\frac{9}{64}$

${(x+\frac{3}{8})}^2=\frac{-71}{64}$

$x+\frac{3}{8}=\sqrt{\frac{-71}{64}}$

$HenceQEhasnorealroots.$