Question

K for x2+2 root2 kx +18=0 has equal roots

Answer 1

$\huge{\boxed{\boxed{\red{\ulcorner{\mid{\overline{\underline{\bf{Answer:-}}}}}\mid}}}}$

$\huge \rightarrow \: k = 3.$

${x}^{2} + 2 \sqrt{2} + 18.$

where,

$a = 1 \: \: \: \: \: \: \: \: \: \: b = 2 \sqrt{2} \: \: \: \: \: \: and \: \: \: c = 18.$

$d = {b}^{2} - 4ac \\ \\ = {(2 \sqrt{2k)} }^{2} - 4 \times 1 \times 18. \\ \\ = 8 {k}^{2} - 72.$

${\star{\underline{\underline {given}}}}$

$d = 0$

$0 = 8 {k}^{2} - 72. \\ \\ \cancel - 8 {k}^{2} = \cancel- 72. \\ \\ 8 {k}^{2} = 72 \\ \\ {k}^{2} = \cancel \frac{72}{8} \\ \\ {k}^{2} = 9. \\ \\ k = 3 \: \: \: \: \: and \: \: \: \: - 3$

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