Question

Dado o polinômio P(x) = x3 – 2x2 + mx – 1, se P(2) = P(1), então qual o valor de m?

Answer 1

P(x) = x3 – 2x2 + mx – 1, se

P(2) = 2^3 – 2(2)^2 + 2m – 1 ==> 8 -8 + 2m - 1 ==> 2m - 1

P(1)= 1^3 – 2(1)^2 + 1.m – 1 ==> 1 - 4 + m - 1 ==>  m - 4

2m - 1 = m - 4 

2m-m = - 4 + 1

m = - 3

Answer 2

Oie, Td Bom?!

>>> Resolvendo os polinômios.

$p(x) = x {}^{3} - 2x {}^{2} + mx - 1$

>>> Substitua: $p(x) = p(2)$ .

$p(2) = 2 {}^{3} - 2 \: . \: 2 {}^{2} + m \: . \: 2 - 1$

$p(2) = 2 {}^{3} - 2 {}^{3} + 2m - 1$

$p(2) = 2m - 1$

>>> Substitua: $p(x) = p(1)$ .

$p(1) = 1 {}^{3} - 2 \: . \: 1 {}^{2} + m \: . \: 1 - 1$

$p(1) = 1 - 2 \: . \: 1 + m \: . \: 1 - 1$

$p(1) = 1 - 2 + m - 1$

$p(1) = - 2 + m$

>>> Resolvendo p(2) = p(1):

$2m - 1 = - 2 + m$

$2m - m = - 2 + 1$

$m = - 1$

Att. Makaveli1996