Question

form the quadratic polynomial whose zeros are 6/5 and 4/25

Answer 1

$\alpha = \frac{6}{5} \\ \beta = \frac{4}{25}$

$\alpha + \beta = \frac{6}{5} + \frac{4}{25} = \frac{30 + 4}{25} = \boxed{\frac{34}{25}}$

$\alpha \beta = \frac{6}{5} \times \frac{4}{25} = \boxed{ \frac{24}{125} }$

$a \: quadratic \: polynomial \: is \: in \: form$

$\: \: \: \: \: \: \: k( {x}^{2} - (\alpha + \beta)x + \alpha \beta )$

$k( {x}^{2} - \frac{34}{25} x + \frac{24}{125} )$

$\frac{1}{125} (125 {x}^{2} - 170x + 24) \\ hence \\ \: polynomial \: is \: (125 {x}^{2} - 170x + 24)$

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