Question

$if \: \alpha \: and \: \beta \: are \: zeros \: of \: polynomial \: 5 {x}^{2} - 7x - 2 \\ \: \: then \: the \: sum \: of \: \\ reciprocals \: of \: zeros \: is - - - - - -$
Provide the solution also with your answer!​

Answer 1

$\huge \mathbb \green{SOLUTION:-}$

$5 {x}^{2} - 7x + 2 \\ Zeros \: can \: be \: determine \\ by \: factorization \: then \\ = > \: 5 {x}^{2} - 5x - 2x + 2 \\ = > \: 5x(x - 1) - 2(x - 1) \\ b(x) = (x - 1)(5x - 2) \\ \therefore \: \alpha = 1 \: and \: \beta = \frac{2}{5} \\ \therefore \: sum \: of \: their \: reciprocal \\ = \frac{1}{1} + \frac{5}{2} \\ = 1 + \frac{5}{2} \\ = \frac{2 + 5}{2} \\ = \frac{7}{2}$