Question

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If $\sf{\alpha \: and \:   \beta \:  are \: the \: zeros \: of   \\   \sf{x}^{2}  - 5x + 6 = 0$

Find a Quadratic Equation whose Zeros are
$\sf \frac{1}{ \alpha } \: and \: \frac{1}{ \beta }$
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Answer 1

Step-by-step explanation:

If $\sf{\alpha \: and \:   \beta \:  are \: the \: zeros \: of   \\   \sf{x}^{2}  - 5x + 6 = 0$

Find a Quadratic Equation whose Zeros are

$\sf \frac{1}{ \alpha } \: and \: \frac{1}{ \beta }$

k = 2 is the answer

Answer 2

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HERE IS UR ANSWER

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Given that

${ \alpha }^{2} + { \beta }^{2} + \alpha \beta = \frac{21}{4} \\ ( \alpha + \beta ) {}^{2} - \alpha \beta = \frac{21}{4}$

$( \frac{ - 5}{2} ) {}^{2} - \frac{k}{2} = \frac{21}{4}$

$\frac{k}{2} = \frac{25}{4} - \frac{21}{4} = 1 \\ k = 2$

given polynomial is k=2