Question

the constant that must be added and subtracted to solve the quadratic equation 2x^2-3x-1=0 by the method of completion of square is?
OPTIONS:
9/16
9
3/4
3​

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{quadratic}\mathrm{equation}\mathrm{is}, \\ 2{\mathrm{x}}^2-3\mathrm{x}-1=0 \\ \Rightarrow 2\left({\mathrm{x}}^2-\frac{3\mathrm{x}}{2}-\frac{1}{2}\right)=0 \\ \Rightarrow {\mathrm{x}}^2-\frac{3\mathrm{x}}{2}-\frac{1}{2}=0 \\ \Rightarrow {\mathrm{x}}^2-\frac{3\mathrm{x}}{2}-\frac{1}{2}+\frac{\mathbf{9}}{\mathbf{16}}-\frac{\mathbf{9}}{\mathbf{16}}=0 \\ \Rightarrow {\mathrm{x}}^2-\frac{3\mathrm{x}}{2}+\frac{9}{16}-\frac{1}{2}-\frac{9}{16}=0 \\ \Rightarrow {\left(\mathrm{x}-\frac{3}{4}\right)}^2-\frac{17}{16}=0 \\ \Rightarrow {\left(\mathrm{x}-\frac{3}{4}\right)}^2=\frac{17}{16} \\ \Rightarrow \mathrm{x}-\frac{3}{4}=\pm \left(\frac{\sqrt{17}}{4}\right) \\ \Rightarrow \mathrm{x}=\frac{3+\sqrt{17}}{4}\mathrm{and}\mathrm{x}=\frac{3-\sqrt{17}}{4} \\ \mathrm{So},\mathrm{the}\mathrm{constant}\mathrm{that}\mathrm{must}\mathrm{be}\mathrm{added}\mathrm{and}\mathrm{subtracted}\mathrm{is}\frac{9}{16}. \end{gathered}$$