Question

if alpha, beta, gamma are zeroes of x^2+3x^2-x-3 then find 1/alpha+1/beta+1/gamma​

Answer 1

Q. If alpha, beta, gamma are zeroes of x³+3x²-x-3 then find 1/alpha+1/beta+1/gamma.

Comparing the given polynomial with ax³+ bx²+cx +d = 0

a=1, b=3, c= -1 and d=-3

$Sum \: of \: zeroes = \alpha + \beta + \gamma = \frac{ - b}{a} = - 3 \\ Product \: of \: zeroes \: taken \: two \: at \: a \: time \\ = \alpha \beta + \beta \gamma + \alpha \gamma = \frac{c}{a} = - 1 \\ Product \: of \: zeroes = \alpha \beta \gamma = \frac{ - d}{a} = 3 \\ now \\ = \frac{1 }{ \alpha } + \frac{1}{ \beta } + \frac{1}{ \gamma } \\ = \frac{ \beta \gamma + \alpha \gamma + \alpha \beta }{ \alpha \beta \gamma } \\ = \frac{ - 1}{3}$