Question

if alpha beta are zeros of polynomial t2-4t+3
find a4b3+b4a3

Answer 1

Answer:

$t {}^{2} - 4t + 3 \\ {t}^{2} - 3t - t + 3 \\ t(t - 3) - 1(t - 3) \\ (t - 1)(t - 3) \\ \alpha = 1 \\ \beta = 3$

$\alpha {}^{4} { \beta }^{3} + { \beta }^{4} { \alpha }^{3} \\ 1 \times 27 + 81 \times 1 \\ 81 + 27 = 108$