Question

Dado o polinômio P(x) = x3 + kx2 + 2x - 5, determine k sendo P(-2) = P(0​

Answer 1

Oie, Td Bom?!

➭$P(x) = x {}^{3} + kx {}^{2} + 2x - 5$

• $x = - 2$:

$P( - 2) = ( - 2) {}^{3} + k \: . \: ( - 2) {}^{2} - 5$

$P( - 2) = - 8 + k \: . \: 4 - 5$

$P( - 2) = - 8 + 4k - 5$

$P( - 2) = - 13 + 4k$

• $x = 0$:

$P(0) = 0 {}^{3} + k \: . \: 0 {}^{2} - 5$

$P(0) = 0 + k \: . \: 0 - 5$

$P(0) = k \: . \: 0 - 5$

$P(0) = 0 - 5$

$P(0) = - 5$

• $P( - 2) = P(0)$:

$- 13 + 4k = - 5$

$4k = - 5 + 13$

$4k = 8$

$k = \frac{8}{4}$

$k = 2$

Att. Makaveli1996