Question

find the quadratic equation whose roots are 2+√3 and 2-√3

Answer 1

Answ

Step-by-step explanation:

Answer 2

Answer:

$Required \: equation:\\x^{2}-4x+1=0$

Step-by-step explanation:

$Let\:\alpha\:and\:\beta \:are\\ roots \: of \:a \: quadratic\: equation$

$Given \: \alpha= 2+\sqrt{3}\\and \: \beta = 2-\sqrt{3}$

$i) Sum \:of \: roots\\ = \alpha+\beta\\=2+\sqrt{3}+2-\sqrt{3}\\=4$

$ii) Product \:of \: roots\\ = \alpha \beta\\=(2+\sqrt{3})(2-\sqrt{3})\\=2^{2}-(\sqrt{3})^{2}\\=4-3\\=1$

$We\:know\:that \\</p><p>Equation \:of \: a \: Quadratic\\eqution \: whose \: roots \:are\:\alpha \\and \: \beta\:is \:x^{2}-(\alpha+\beta)x+\alpha \beta =0$

$Now, Required \: equation:\\x^{2}-4x+1=0$

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