Question

considerado que p(x)= 2x3 - kx2 +3x -2k para qual valores de k temos p(2) =4?

Answer 1

4 = 2 * 2³ -k * 2² +3 * 2 -2k

4 = 16 -4k +6 -2k

4 = 22 -6k

6k = 22 -4

k = 18/6

k = 3

Answer 2

$p(x) = 2x {}^{3} - kx {}^{2} + 3x - 2k \\ \boxed{p(2) = 4} \\ 4 = 2 \: . \: 2 {}^{3 } - k \: . \: 2 {}^{2} + 3 \: . \: 2 - 2k \\ 4 = 2 \: . \: 8 - k \: . \: 4 + 3 \: . \: 2 - 2k \\ 4 = 16 - 4k + 6 - 2k \\ 4 = 22 - 6k \\ 6k = 22 - 4 \\ 6k = 18 \\ k = \frac{18}{6} \\ \boxed{\boxed{\boxed{k = 3}}}$

atte. yrz