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

$\textbf{Solution}$

Given polynomial

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

On comparing with ax^3 + bx^2 + cx + d we get

a = 1 , b = - 14 , c = 37 , d = - 60

i ) Sum of zeroes = - b / a

$\alpha + \beta + \gamma = \frac{ - b}{a}$


$\alpha + \beta + \gamma = \frac{14}{1} \\ \\ \alpha + \beta + \gamma = 14$

ii ) Sum of product of zeroes = c / a

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

iii ) Product of zeroes = - d / a

$\alpha \beta \gamma = \frac{ - d}{a}$
$\alpha \beta \gamma = 60$

$\textbf{Hope it helps!!}$