Question

write a quadratic polynomial whose zeros are root3 and-root3

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{\alpha }=\sqrt{3}\mathrm{and}\mathrm{\beta }=-\sqrt{3} \\ \mathrm{Now},\mathrm{\alpha }+\mathrm{\beta }=\sqrt{3}+\left(-\sqrt{3}\right)=0 \\ \mathrm{Now},\mathrm{\alpha \beta }=\sqrt{3}\times \left(-\sqrt{3}\right)=-3 \\ \mathrm{Now},\mathrm{required}\mathrm{polynomial}\mathrm{is} \\ \mathrm{p}\left(\mathrm{x}\right)=\mathrm{k}\left[{\mathrm{x}}^2-\left(\mathrm{\alpha }+\mathrm{\beta }\right)\mathrm{x}+\mathrm{\alpha \beta }\right],\mathrm{where}\mathrm{k}\mathrm{is}\mathrm{a}\mathrm{non}\mathrm{zero}\mathrm{real}\mathrm{number} \\ =\mathrm{k}\left[{\mathrm{x}}^2-0\mathrm{x}-3\right] \\ ={\mathrm{x}}^2-3\left[\mathbf{On}\mathbf{}\mathbf{taking}\mathbf{}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\right] \end{gathered}$$