Question

Find a quadratic polynpmial whose product and sum of the zeroes are -13/5 and -3/5 respectively

Answer 1

$\bold \red \star \: \underline{Given:-} \begin{cases} \sf{ \underline{Zero \: are:-}} \\ \sf{Product = \frac{ - 13}{5} } .\\ \sf{Sum = \frac{ - 3}{5}}. \end{cases}$

$\bold \red \star \: \underline{Solution:-}$

$Let \: first \: zero \: be \: \blue{\alpha} \: and \: \pink{ \beta }.$

$\blue {\alpha + \beta }= \frac{ - 3}{5}$

$\pink {\alpha \times \beta }= \frac{ -13}{5}$

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$\red{k }({x}^{2} - Sx + P.) \\ \\ \red{k} \{ {x}^{2} - ( \frac{ - 3}{5} )x + ( \frac{ - 13}{5} ) \} \\ \\ \red{k}\{ {x}^{2} - ( \frac{ - 3x - 13}{5} ) \} \\ \\ \red{k}(5 {x}^{2} + 3x - 13.)$

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$Our \: \: polynomial \: \: become$

$\: \: \: \: \: \: \: \: \: \purple{ \boxed {\huge {\large \boxed{5 {x}^{2} + 3x - 13.}}}}$