Question

find a quadratic polynomial the sum and product of its zeroes are root2 and -3/2 respectively

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{We}\mathrm{are}\mathrm{given}\mathrm{that}\mathrm{sum}\mathrm{of}\mathrm{zeroes}\left(\mathrm{S}\right)\mathrm{is}\sqrt{2}\mathrm{and}\mathrm{product}\mathrm{of}\mathrm{zeroes}\left(\mathrm{P}\right)\mathrm{is}-\frac{3}{2} \\ \mathrm{Now},\mathrm{the}\mathrm{required}\mathrm{polynomial}\mathrm{is}, \\ \mathrm{p}\left(\mathrm{x}\right)=\mathrm{k}\left[{\mathrm{x}}^2-\mathrm{Sx}+\mathrm{P}\right],\mathrm{where}\mathrm{k}\mathrm{is}\mathrm{a}\mathrm{non}\mathrm{zero}\mathrm{real}\mathrm{number} \\ =\mathrm{k}\left[{\mathrm{x}}^2-\sqrt{2}\mathrm{x}-\frac{3}{2}\right] \\ =\frac{\mathrm{k}}{2}\left[2{\mathrm{x}}^2-2\sqrt{2}\mathrm{x}-3\right] \\ =2{\mathrm{x}}^2-2\sqrt{2}\mathrm{x}-3\left[\mathbf{On}\mathbf{}\mathbf{taking}\mathbf{}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}\right] \\ \mathrm{Regards}. \end{gathered}$$