Question

4√3x^2 +5x -2√3 solve for x by quadratic formula​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given equation :-

• $\sf \: \: \: \: \: 4 \sqrt{3} {x}^{2} + 5x - 2 \sqrt{3} .$

Let's find Discriminant of this equation by using the formula:-

$:\implies\underline\purple{\boxed{\sf D = b²-4ac}}$

$\implies\sf D = ( 5) ^{2} - 2(4√3)( -2√3) \\ \\ \implies\sf D = 25+96 =121$

• Since, D>0 hence, this equation will have distinct and real roots.

Formula to be applied now is as follows:-

$\implies\underline\pink{\boxed{\sf x = \dfrac{-b±√D}{2a}}}$

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$\\ \colon\implies{\underline{\boxed{\sf{ x = \dfrac{ -b \pm \sqrt{ b^2 - 4ac} }{2a} }}}}$

⠀$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 5\pm \sqrt{ {(5)}^{2} - 4 \times 4 \sqrt{3} \times - 2 \sqrt{3} } }{2 \times 4 \sqrt{3} }$

$\sf\: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 5\pm \sqrt{ 25 + 96 } }{ 8 \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 5\pm \sqrt{ 121 } }{ 8 \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \purple{ : \implies x = \dfrac{ - 5\pm 11 }{ 8 \sqrt{3} }}$

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$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 5 + 11 }{ 8 \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \implies x = \dfrac{ 6}{ 8 \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{3 }{ 4 \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{3 \sqrt{3} }{ 12}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \red{: \implies x = \dfrac{\sqrt{3} }{ 4 } }$

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$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 5 - 11 }{ 8 \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 16 }{ 8 \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies x = \dfrac{ - 2}{ \sqrt{3} }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: : \red{ \implies x = \dfrac{ - 2 \sqrt{3} }{ 3 }}$