Question

Find the zeros of the polynomial p(x)= x3-5x2-16x+80

Answer 1

$p(x) = x {}^{3} - 5x {}^{2} - 16x + 80$

Let the zeroes be :
$\alpha \: \beta \: and \: \gamma$

$let \: \gamma = - \alpha$

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

$= \frac{ 5}{1}$

$\beta = 5$

$\alpha \times \beta \times ( - \gamma ) = \frac{ - d}{a}$

$\alpha \times \beta \times ( - \gamma ) = \frac{ - 80}{1}$

$- \alpha {}^{2} \times 5 = - 80$

$\alpha {}^{2} = \frac{ - 80}{ - 5}$

$\alpha {}^{2} = 16$

$\alpha = 4$

$\gamma = - \alpha$

$\gamma = - 4$
Zeroes are 5, 4 and -4