Question

find the value of k for which the quadratic equation 2 X square + kx + 3 equal to zero has turial equation roots​

Answer 1

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

$\green{\tt{\therefore{Value\:of\:k=\pm 2\sqrt{6}}}}$

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

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

• According to given question :

$\tt{ : \implies 2x^{2} +kx + 3= 0} \\ \\ \tt{\circ \: a = 2} \\ \\ \tt{\circ \: b = k}\\\\ \tt{\circ \:c = 3}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (k)^{2} - 4\times2 \times 3= 0 } \\ \\ \tt{: \implies \: {k}^{2} -24= 0 } \\ \\ \tt{ : \implies \: ({k}^{2} -( 2\sqrt{6})^{2}) = 0 } \\\\ \tt{: \implies (k+2\sqrt{6})(k-2\sqrt{6})= 0} \\ \\ \green{\tt{: \implies k = \pm 2\sqrt{6} }}$