Question

find the value of k for which quadratic equation 3 x square minus kx + 5 is equal to zero has two equal roots

Answer 1

hope this will help you

Answer 2

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

$\green{\tt{\therefore{Value\:of\:k=\pm 2\sqrt{15}}}}$

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

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies 3x^{2} -kx +5 = 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies 3x^{2} -kx +5= 0} \\ \\ \tt{\circ \: a = 3} \\ \\ \tt{\circ \: b = -k}\\\\ \tt{\circ \:c = 5}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (-k)^{2} - 4\times3 \times 5= 0 } \\ \\ \tt{: \implies \: {k}^{2} -60 = 0 } \\ \\ \tt{ : \implies \: ({k}^{2} - (2\sqrt{15})^{2}) = 0 } \\\\ \tt{: \implies (k-2\sqrt{15})(k+2\sqrt{15})} \\ \\ \tt{: \implies k=2\sqrt{15}\:and\:-2\sqrt{15}} \\ \\ \green{\tt{: \implies k = \pm 2\sqrt{15} }}$