Question

plzzzz help me !!!!​

Answer 1

Answer:-

$\tt { \boxed{ \underline{ \pink{ \tt{ \: - 3 \sqrt{3} and \: \dfrac{ - 2 \sqrt{3} }{3} \:}}}}}$

$\sf \huge \underline \blue{Question}$

Find the roots of the polynomial

$\rm{ \sqrt{3} {x}^{2} + 11x + 6 \sqrt{3}}$

$\sf \underline \pink{step \: by \: \: step \: explanation}$

$\rm \purple{ \implies \: \sqrt{3} {x}^{2} + 11x + 6 \sqrt{ 3 }}$

$\rm \orange{ \implies \: \sqrt{3} {x}^{2} + 11x + 6 \sqrt{3} = 0}$

$\rm \green{ \implies \: \sqrt{3} {x}^{2} + 9x + 2x + \sqrt{3} = 0}$

$\rm \blue{ \implies \: \sqrt{3}x(x + 3 \sqrt{3}) + 2(x + 3 \sqrt{3}) = 0}$

$\rm \pink{ \implies \: (x + 3 \sqrt{3})( \sqrt{3}x + 2) = 0}$

$\rm \red{ \implies \: x + 3 \sqrt{ 3} = 0 \: \: or \: \: \sqrt{3x} + 2 = 0}$

$\rm \green{ \implies \: x = - 3 \sqrt{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ \: \: \: \: \: \: \: \: \: or}$

$\rm \purple{ \implies \: x = \dfrac{ \sqrt{ \sqrt{2} } }{ \sqrt{3} } = \dfrac{ - 2 \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \dfrac{ - 2 \sqrt{3} }{3}}$

so,

roots of equation are,

$\tt \red{ \: - 3 \sqrt{3} and \: \dfrac{ - 2 \sqrt{3} }{3}}$

Answer 2

$\tt { \boxed{ \underline{ \pink{ \tt{ \: - 3 \sqrt{3} \: and \: \dfrac{ - 2 \sqrt{3} }{3} \:}}}}} \\ \sf \huge \underline\blue{Question} \\ \rm{ \sqrt{3} {x}^{2} + 11x + 6 \sqrt{3}}\\\rm \purple{ \implies \: \sqrt{3} {x}^{2} + 11x + 6 \sqrt{ 3 }} \\\rm \orange{ \implies \: \sqrt{3} {x}^{2} + 11x + 6 \sqrt{3}} \\ \rm \green{ \implies \: \sqrt{3} {x}^{2} + 9x + 2x + \sqrt{3} = 0} \\ \rm \blue{ \implies \: \sqrt{3}x(x + 3 \sqrt{3}) + 2(x + 3 \sqrt{3}) = 0} \\ \rm \pink{ \implies \: (x + 3 \sqrt{3})( \sqrt{3}x + 2) = 0} \\ \rm \red{ \implies \: x + 3 \sqrt{ 3} = 0 \: \: or \: \: \sqrt{3x} + 2 = 0} \\ \rm \green{ \implies \: x = - 3 \sqrt{3} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ \: \: \: \: \: \: \: \: \: or} \\ \rm \purple{ \implies \: x = \dfrac{ \sqrt{ \sqrt{2} } }{ \sqrt{3} } = \dfrac{ - 2 \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \dfrac{ - 2 \sqrt{3} }{3}} \\ \\ \tt \red{ \: - 3 \sqrt{3} and \: \dfrac{ - 2 \sqrt{3} }{3}}$