Question

find the value of k for which the quadratic equation 16 X square + 4 kx + 9 equals to zero has real and equal roots​

Answer 1

Step-by-step explanation:

Hope it is the correct answer

Answer 2

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

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

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

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies 16x^{2} +4kx + 9 = 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies 16x^{2} +4kx + 9= 0} \\ \\ \tt{\circ \: a =16} \\ \\ \tt{\circ \: b = 4k}\\\\ \tt{\circ \:c = 9}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (4k)^{2} - 4\times16 \times 9= 0 } \\ \\ \tt{: \implies \: 16{k}^{2} -576 = 0 } \\ \\ \tt{ : \implies \: 16({k}^{2} - 36) = 0 } \\\\ \tt{: \implies k^{2}= 36} \\ \\ \tt{: \implies k= \sqrt{36}} \\ \\ \green{\tt{: \implies k = \pm 6 }}$