Question

Show that the equation $x^2-x+2=0$ has no real roots.

Answer 1

$$\begin{gathered} \text{Given:}{x}^2-x+2=0 \\ \text{Here,} \\ a=1,b=-1\mathrm{and}c=2 \\ \mathrm{Discriminant}D\mathrm{is}\mathrm{given}\mathrm{by}: \\ D=(b^2-4ac) \\ \text{=}{(-1)}^2-4\times 1\times 2 \\ \text{= 1}-8 \\ \text{=}-7<0 \\ D<0;\mathrm{therefore},\text{the roots of the equation are not real}\text{.} \end{gathered}$$