Question

example of a quadratic polynomial with no real zeros

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{f}\left(\mathrm{x}\right)=2{\mathrm{x}}^2+3\mathrm{x}+2 \\ \mathrm{Comparing}\mathrm{it}\mathrm{with}{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c},\mathrm{we}\mathrm{get} \\ \mathrm{a}=2;\mathrm{b}=3;\mathrm{c}=2 \\ \mathrm{Now},\mathrm{D}={\mathrm{b}}^2-4\mathrm{ac}={\left(3\right)}^2-4\left(2\right)\left(2\right)=9-16=-7<0 \\ \mathrm{Since},\mathrm{D}<0,\mathrm{so}\mathrm{the}\mathrm{given}\mathrm{polynomial}\mathrm{has}\mathrm{no}\mathrm{real}\mathrm{zeroes}. \end{gathered}$$