Question

$if \: \: sum \: \: of \: \: roots \: \: is \: 5 \: \: then \: \: find \: \\ k \: for \: \: given \: \: equation \: \: - \\ \\ k {x}^{2} - 4 {k}^{2} + 5 = 0$
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Answer 1

${ \bold{ \underline{ \green{ANSWER} }: - }}$

${ \bold{ \underline{Given} : - }} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: . \: \: a \: \: quadratic \: \: equation \: \: k {x}^{2} - 4 {k}^{2} x+ 5 = 0 }}} \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: . \: \: sum \: \: of \: \: roots = 5}}} \\ \\ { \bold{ \underline{To \: \: find} : - }} \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: value \: \: of \: \: k}}} \\ \\ { \bold{ \underline{used \: \: formula} : - }} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: \: . \: \: sum \: \: of \: \: roots \: = - \frac{b}{a} }}} \\ \\ \\ { \bold{ \huge{ \boxed{ \boxed{ \red{ \bigstar \: solution \bigstar}}}}}} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: . \: \: here \: \: \: - \: \: }}} \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: . \: \: a = k}}} \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: . \: \: b = - 4 {k}^{2} }}} \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: . \: \: c = 5}}} \\ \\{ \bold{ \orange{ \implies \:sum \: \: of \: \: roots = - \frac{b}{a} }}}\\ \\ { \bold{ \orange{ \implies \: - \frac{b}{a} = 5 }}} \\ \\ { \bold{ \orange{ \implies \: - (\frac{ - 4 {k}^{2} }{k} ) = 5}}} \\ \\ { \bold{ \orange{ \implies \: \cancel \frac{4 {k}^{2} }{k} = 5 }}} \\ \\ { \bold{ \orange{ \implies \:4k = 5 }}} \\ \\ { \bold{ \orange{ \implies \: { \boxed{k = \frac{5}{4} }}}}}$

Answer 2

$\huge {\bold {\pink {Given :}}}$

$<b ><font color ="pink" ><font size ="5" >$

$\alpha + \beta = 5$

$</b ></font ></font>$

$\huge {\bold {\pink {To\: find :}}}$

$<b ><font color ="pink" ><font size ="5" >$

$Value \:of \: "k "$

$</b ></font ></font >$

$\huge {\bold {\pink{ So,}}}$

$<b ><font color ="pink" ><font size ="5" >$

$= > \alpha + \beta = - \frac{b}{a} \\ \\ = > 5 = - \frac{ (- 4 {k}^{2} )}{k} \\ \\ = > 5 = 4k \\ \\ = > k = \frac{5}{4}$

$</b ></font ></font >$

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$\huge {\bold {\red {Hope \: it \: helps}}}$