Question

using facterisation find the roots of the quadratic equation y²+2root3y+3=0


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Answer 1

$\huge\bf\color{navy}{{\underline{Question}}:}$

$\sf Using \: factorisation, \: find \: the \: roots \\ \sf of \: the \: quadratic \: equation: \\ \bf {y}^{2} + 2 \sqrt{3} y + 3$

$\huge\bf\color{navy}{{\underline{Answer}}:}$

$\bf{Here,~S=2{\sqrt{3}}~~~and~~~p=3}$

$\bf{~~~~~~~~~~~~\therefore~({\sqrt{3}},{\sqrt{3}})}$

$\bf{~~~~~(y^{2}+{\sqrt{3}}y)+({\sqrt{3}}y+3)}$

$\bf{→[y(y+{\sqrt{3}})]+[{\sqrt{3}}(y+{\sqrt{3}})]}$

$\bf{→(y+{\sqrt{3}})(y+{\sqrt{3}})}$

$\bf{→y+{\sqrt{3}}=0~~,~~or~~y+{\sqrt{3}}=0}$

$\bf{→y=-{\sqrt{3}}~~and~~y=-{\sqrt{3}}}$

$\bf{~~\therefore~Roots~are:~-{\sqrt{3}}~and~-{\sqrt{3}}}$

$\huge\bold\color{navy}{Hope~it~helps..!!}$