Question

if the zeroes of the polynomial x^3-14x^2+37x-60 are alpha,beta,gamma,then find
(i) alpha +beta+ gamma
(ii) alpha beta+beta gamma+gamma alpha
(iii) alpha beta gamma

Answer 1

$\\\implies x^{3}-14x^{2}+37x-60$

$\\ \implies in\: equation \\\\ax^{3}+bx^{2}+cx+d \\\\ \alpha+\beta+\gamma= \frac{-b}{a}\\\\ \alpha\beta+\beta\gamma+\gamma\alpha= \frac{c}{a}\\\\ \alpha\beta\gamma = \frac{-d}{a}$

$(1)x^{3} + (-14)x^{2} + (37)x + (-60) \\\\a=1\\b=-14\\c=37\\d=-60$

$\alpha+\beta+\gamma\\= \frac{-b}{a}\\=\frac{+14}{1}\\\boxed{\implies{14}}$

$\alpha\beta+\beta\gamma+\gamma\alpha= \frac{c}{a}\\=\frac{37}{1} \\\boxed{\implies{37}}$

$\\\alpha\beta\gamma = \frac{-d}{a}\\=\frac{+60}{1}\\\boxed{\implies{60}}$