Question

if
$\alpha \: \beta \gamma$
are the three zeroes of the polynomial and
$p(x) \: \: \: = \: x {}^{3} - \: 64x \: - 14$
then what is the value of

${ \alpha }^{3} + \: { \beta }^{3} \: + { \gamma }^{3}$

​

Answer 1

Hey,

$f(x) = x {}^{3} - 64x - 14 \\ \\ \alpha \beta \gamma = - ( - 14) = 14 \\ \\ now \\ \alpha { }^{3} + \beta {}^{3} + \gamma {}^{3 } = 3 \alpha \beta \gamma = 3 \times 14 = 42$
Hope it helps you!!!