Question

Find the nature of the roots of the following quadratic quadratic equations if the real roots exist find them 2 x square - 3 x + 5 is equal to zero

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{equation}\mathrm{is}, \\ 2{\mathrm{x}}^2-3\mathrm{x}+5=0 \\ \mathrm{Now},\mathrm{comparing}\mathrm{it}\mathrm{with}{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,\mathrm{we}\mathrm{get} \\ \mathrm{a}=2;\mathrm{b}=-3;\mathrm{c}=5 \\ \mathrm{Now},\mathrm{D}={\mathrm{b}}^2-4\mathrm{ac} \\ ={\left(-3\right)}^2-4\times 2\times 5 \\ =9-40 \\ =-31<0 \\ \mathrm{Since},\mathrm{D}<0,\mathrm{so}\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{has}\mathrm{no}\mathrm{real}\mathrm{roots}. \end{gathered}$$

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