Question

if (5-√3) is one f the roots of quadratic equation x2-10x+2k=0, find the value of k​

Answer 1

Answer (~_^)

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$\huge \pink{ \boxed { \blue { \mathfrak{ \overbrace { \overbrace{ \fcolorbox{pink}{aqua}{ \underline{}{ \underline { \pink{ \ddag \: question \ddag}}}}}}}}}}$

$\: \: \: \: \: \: \:\clubsuit \bf { \red{if \: (5 - \sqrt{3} ) \: is \: one \: of \: \: the \: root \: of \: the \: quadratic \: equation}}$

$\: \: \: \: \:\clubsuit \bf{ \purple{given \: equation \to \ \: {x}^{2} - 10x + 2k = 0}}$

$\: \: \: \: \: \:\mapsto \sf{ \: put \: the \: root \: in \: this \: given \: equation}$

$\: \: \: \: \ \: \:\mapsto \sf{ {(5 - \sqrt{3)} }^{2} - 10(5 - \sqrt{3} ) + 2k = 0}$

$\: \: \: \: \:\mapsto \sf{(25 + 3 - 10 \sqrt{3} ) - 50 + 10 \sqrt{3} + 2k = 0}$

$\: \: \: \: \: \: \mapsto \sf{28 - 10 \sqrt{3} - 50 + 10 \sqrt{3} + 2k = 0}$

$\: \: \: \: \: \: \: \mapsto \sf{28 - 50 - \cancel \pink {10 \sqrt{3} + 10 \sqrt{3} } + 2k = 0}$

$\: \: \: \: \: \:\mapsto \sf{ - 22 + 2k = 0}$

$\: \: \: \: \: \: \mapsto \sf{2k = 22}$

$\: \: \: \: \: \: \mapsto \sf{k = \cancel \red{ \frac{22}{2} } = 11}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red \bigstar \boxed { \sf \pink{k = 11 \: is \: the \: correct \: answer}}$

don't thanks this question OK guys .......