Question

Without finding the roots comment on the nature of the
roots of the quadratic equation.
3 x² -- 6x + 5 = 0

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{quadratic}\mathrm{equation}\mathrm{is}, \\ 3x^2-6x+5=0 \\ \mathrm{Comparing}\mathrm{it}\mathrm{with}a{x}^2+bx+c=0 \\ a=3;b=-6;c=5 \\ \mathrm{Now},D=b^2-4ac={\left(-6\right)}^2-4\left(3\right)\left(5\right)=36-60=-24<0 \\ \mathrm{So},\mathrm{the}\mathrm{roots}\mathrm{are}\mathrm{not}\mathrm{real}. \end{gathered}$$