Question

determine the nature of roots of the quadratic equation 3/5x square -2/3x + 1 = 0

Answer 1

$$\begin{gathered} \frac{3{\mathrm{x}}^2}{5}-\frac{2\mathrm{x}}{3}+1=0 \\ \Rightarrow \frac{9{\mathrm{x}}^2-10\mathrm{x}+15}{15}=0 \\ \Rightarrow 9{\mathrm{x}}^2-10\mathrm{x}+15=0 \\ \mathrm{Now},\mathrm{a}=9;\mathrm{b}=-10;\mathrm{c}=15 \\ \mathrm{Now},\mathrm{D}={\mathrm{b}}^2-4\mathrm{ac}={\left(-10\right)}^2-4\left(9\right)\left(15\right)=100-540=-440<0 \\ \mathrm{Since},\mathrm{D}<0,\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{has}\mathrm{no}\mathrm{real}\mathrm{roots}. \end{gathered}$$