Question

Find a quadratic polynomial whose zeros are 2 root 3- 2 root 3

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{S}\mathrm{and}\mathrm{P}\mathrm{be}\mathrm{the}\mathrm{sum}\mathrm{and}\mathrm{product}\mathrm{of}\mathrm{zeros}\mathrm{respectively}. \\ \mathrm{So},\mathrm{S}=2\sqrt{3}+\left(-2\sqrt{3}\right)=2\sqrt{3}-2\sqrt{3}=0 \\ \mathrm{P}=2\sqrt{3}\times \left(-2\sqrt{3}\right)=-12 \\ \mathrm{So},\mathrm{the}\mathrm{required}\mathrm{polynomial}\mathrm{whose}\mathrm{zeros}\mathrm{are}2\sqrt{3}\mathrm{and}\left(-2\sqrt{3}\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ ={\mathrm{x}}^2-\mathrm{Sx}+\mathrm{P} \\ ={\mathrm{x}}^2-\left(0\times \mathrm{x}\right)+\left(-12\right) \\ ={\mathrm{x}}^2-12 \end{gathered}$$
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