Question

Find the value of k for
kx(x-2)+6=0

Answer 1

Hello......
here is the answer.
kx(x--2)+6=0
kx^2-2kx+6=0
in this equation, a=k, b=-2k, c=6
by quadratic formula
b^2-4ac=o.
we get k=6

Answer 2

$\fbox{ \sf \huge \underline{solution}} \hookrightarrow \huge$

$\sf{kx {}^{2} - 2kx \: + 6 = 0 }$

$\sf \implies {kx {}^{2} - 2kx \: + 6 = 0} \: \: \: \: \: ...(in \: the \: standard \: from)$

$\sf{here, \: a = k, \: b = - k, \: c= 6}$

$\sf \triangle{ \implies = b {}^{2} - 4ac }$

$\sf{ \implies( - 2k) {}^{2} - 4 \: (k)(6) }$

$\sf{ \implies 4k {}^{2} - 24k }$

$\sf {the \: root \: are \: real \: and \: equal. }{\: \: \: \: \: \: \: \: \: ...(given)}$

$\sf{ \implies \triangle = 0}$

$\sf{ \implies4k {}^{2} - 24k = 0}$

$\sf{ \implies4k(k - 6) = 0}$

$\sf{ \implies4k = 0 \: or \: \: k - 6 = 0}$

$\sf{ \implies \: k = 0 \: or \: k = 6}$

$\sf{k = 0 \: is \: unacceptable, \: because \: if \: k = 0,} \\ \sf{the \: coefficient \: of \: the \: quadratic \: term \: becomes \: zero.} \\ \sf{hence, \: the \: equation \: will \: not \: be \: a \: quadratic \: equation.}$

$\fbox{ \sf \huge \underline{k = 6}}$

$\sf \huge \underline{ans \leadsto\: the \: value \: of \: k \: is \: 6.}$

HOPE IT'S HELP