Question

Show that the equation $2x^2-5x-4=0$ has real and unequal roots.

Answer 1

$$\begin{gathered} \text{We have to show that the roots of the equation (}2x^2-5x-4=0)\text{are real and unequal}\text{.} \\ \mathrm{For}\mathrm{real}\mathrm{and}\mathrm{unequal}\mathrm{roots},\mathrm{we}\mathrm{have}: \\ D>0 \\ or{b}^2-4ac>0 \\ \mathrm{Here}, \\ b=-5,a=2\mathrm{and}c=-4 \\ \therefore b^2-4ac=(-5{)}^2-4\times 2\times (-4) \\ =25+32 \\ =57>0 \\ \mathrm{For}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{D}>0;\mathrm{therefore},\mathrm{the}\mathrm{roots}\mathrm{are}\mathrm{real}\mathrm{and}\mathrm{unequal}. \end{gathered}$$