Question

find the value of K for which the quadratic equation 3x^2 - root3 kx+4=0 has equal roots

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:k=\pm 4}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies 3x^{2} -\sqrt{3}kx + 4= 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies 3x^{2} -\sqrt{3}kx + 4= 0} \\ \\ \tt{\circ \: a = 3} \\ \\ \tt{\circ \: b = -\sqrt{3}k}\\\\ \tt{\circ \:c = 4}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (-\sqrt{3}k)^{2} - 4\times3\times 4= 0 } \\ \\ \tt{: \implies \: 3{k}^{2} -48 = 0 } \\ \\ \tt{ : \implies \: 3({k}^{2} - 16) = 0 } \\\\ \tt{: \implies k^{2}= 16} \\ \\ \tt{: \implies k= \sqrt{16}} \\ \\ \green{\tt{: \implies k = \pm 4 }}$