Question

Q. Find Quadratic equation whose roots are 2 + root3 and 2 - root3 .

Answer 1

Dear Student.

$$\begin{gathered} Therootsoftheequationaregiventobe2+\sqrt{3}and2-\sqrt{3} \\ Wecanwriteitas(x-(2+\sqrt{3}\left)\right)(x-(2-\sqrt{3}\left)\right)=0 \\ i.e.(x-2-\sqrt{3})(x-2+\sqrt{3})=0 \\ x(x-2+\sqrt{3})-2(x-2+\sqrt{3})-\sqrt{3}(x-2+\sqrt{3})=0 \\ {x}^2-2x+\sqrt{3}x-2x+4-2\sqrt{3}-\sqrt{3}x+2\sqrt{3}-3=0 \\ {x}^2-4x+1=0 \\ Hence,thisistherequiredquadraticequation. \end{gathered}$$

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