Question

find the value of k so that eqn 3x^2+kx-2=0 has roots whose sum is equal to 6​

Answer 1

${ \bold{ \boxed{ \boxed { \mathfrak{ \red{ \huge{ \huge{answer}}}}}}}}$

${ \bold{ \underline{Given \: \: quadratic \: \: equation} : - }} \\ \\ \\ { \bold{ \orange{ \mathtt{ \implies \: \: 3 {x}^{2} + kx - 2 = 0}}}}$

${ \bold{ \underline{To \: \: find} : - }} \\ \\ \\ { \bold{ \orange{ \mathtt{ \implies \: value \: \: of \: \: \: k \: }}}}$

${ \bold{ \red{ \mathtt{ \underline{used \: \: formula} : - }}}} \\ \\ { \bold{ \orange{ \mathtt{ (1) \: \: sum \: \: of \: \: roots \: \: = - \frac{b}{a} }}}}$

${ \bold{ \boxed{ \boxed{ \green{ \huge \: \star \: solution \star}}}}}$

${ \bold{ \orange{ \mathtt{ \: \implies \: sum \: \: of \: \: roots \: \: = - \frac{b}{a} = - \frac{k}{3} = 6 }}}} \\ \\ { \bold{ \orange{ \mathtt{ \: \implies \: - \frac{k}{3} = 6 }}}} \\ \\ { \bold{ \orange{ \mathtt{ \: \implies \: { \boxed{k = - 18}}}}}}$

${ \bold{ \underline{ Extra \: \: knowledge } : - }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: { \bold{ \mathtt{ \blue{. \: \: multiply \: \:of \: \: roots = \frac{c}{a} }}}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: { \bold{ \mathtt{ \blue{ . \: difference \: \: of \: \: roots = \frac{ \sqrt{d} }{a} }}}}$

Answer 2

⠀⠀⠀⠀$\huge\underline{ \overline{ \bf{ \purple{QUESTION}}}}$

find the value of k so that eqn 3x^2+kx-2=0 has roots whose sum is equal to 6

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⠀⠀⠀⠀⠀$\huge\underline{ \underline{ \bf{ { \blue{ an{ \pink{sw{ \purple{er \: : = }}}}} }}}}$

$\large\underline{ \underline{ \green{ \bold {given}}}} = >$

$\bf \large \: a = 3 \\ \bf \large \:b = k \\ \bf \large \: c = - 2$

$\bf \large \: sum \: of \: roots \: = 6$

$\large\underline{ \underline{ \green{ \bold{solution}}}} = >$

$\bf \large \: \alpha + \beta = 6 \ \\ \ <strong>=</strong><strong>=</strong><strong>></strong> \bf \large6 = \frac{ - k}{3} \\ \ \\ <strong>=</strong><strong>=</strong><strong>></strong>\bf \large 6 \times 3 = - k \\ \\ \large \:{ \boxed{ \fbox{ \purple{ \bf{k =-18 }}}}}$

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hops this may help you

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$\huge \blue{ \mathfrak{thanks♡</p><p>}}$