Question

if alpha , beta , meta are the zeroes of the polynomial ax^3+bx^2 +c x+d then find 1/alpha + 1/ beta +1/meta =
plzz answer fastly urgent

Answer 1

$ax^3+bx^2+cx+d$

From Vieta's formila we have
$\alpha\beta+\beta\gamma+\gamma\alpha=\dfrac{c}{a}$
$\alpha\beta\gamma=-\dfrac{d}{a}$

Now take the given expression
$\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}\\~\\=\dfrac{\alpha\beta+\beta\gamma+\gamma\alpha}{\alpha\beta\gamma}\\~\\=\dfrac{\frac{c}{a}}{-\frac{d}{a}}\\~\\=-\frac{c}{d}$