Question

find the value of k in which the quadratic equation is X square + 2 root 2kx+18=0.has equal roots​

Answer 1

Answer:

k =3

Step-by-step explanation:

${x}^{2} + 2 \sqrt{2} kx + 18 = 0 \\ a = 1 \\ b = 2 \sqrt{2}k \\ c = 18 \\ d = {b}^{2} - 4ac \\ 0 = {(2 \sqrt{2}) }^{2} - 4(1)(18) \\ 0 = 8 {k}^{2} - 72 \\ 8 {k}^{2} = 72 \\ {k }^{2} = 9 \\ k = 3$

Answer 2

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

$\green{\tt{\therefore{Value\:of\:k=\pm 3}}}$

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

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies x^{2} +2\sqrt{2}kx + 18 = 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies x^{2} +2\sqrt{2}kx + 18= 0} \\ \\ \tt{\circ \: a = 1} \\ \\ \tt{\circ \: b = 2\sqrt{2}k}\\\\ \tt{\circ \:c = 18}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (2\sqrt{2}k)^{2} - 4\times1 \times 18= 0 } \\ \\ \tt{: \implies \: 8{k}^{2} -72 = 0 } \\ \\ \tt{ : \implies \: 8({k}^{2} - 9) = 0 } \\\\ \tt{: \implies k^{2}= 9} \\ \\ \tt{: \implies k= \sqrt{9}} \\ \\ \green{\tt{: \implies k = \pm 3 }}$