Question

If one of the zeroes of the cubic polynomial $x^3+a{x}^2+bx+c$ is $-1$ then product of the other two zeroes is?

Answer 1

$\to a=\alpha +\beta -1$

$b=\alpha \beta -\beta -\alpha$ $\to$ Property

$c=-\alpha \beta$

Also$-1+a-b+c=0$

$0-b+c=1$

$\therefore -\alpha -\beta +1-\alpha \beta +\beta +\alpha -\alpha \beta =1$

$\therefore 1-2\alpha \beta =1$

$\therefore \alpha \beta =0$