Question

alpha and beta are zeroes of the polynomial 3x^+2x+3 then find 1/alpha^+ 1/beta^​

Answer 1

Answer:

$zeroes \: (roots) \: : \: \alpha \: \: and\: \: \beta \\ product \: of \: zeroes = \alpha \beta \\ = \frac{constant \: term}{coeffecient \: of \: {x}^{2} } = \frac{3}{3} = 1 \\s um \: of \:z eroes \: = \alpha + \beta \\ = \frac{coeffecient \: of \: x}{coeffecient \: of {x}^{2} } = \frac{2}{3 } \\ = > > \\ \frac{ \alpha + \beta }{ \alpha \beta } = \frac{ \alpha }{ \alpha \beta } + \frac{ \beta }{ \alpha \beta } \\ = \frac{1}{ \beta } + \frac{1}{ \alpha } \\ = \frac{ \frac{2}{3} }{1} = \frac{2}{3}$