Question

Determina o valor de k de modo que x=1 seja raiz do polinómio p(x)=x³+(k-3)x²-x+5​

Answer 1

Resposta:

p(1): 1³ + (k - 3) . 1² - 1 + 5 = 0

p(1): 1 + (k - 3) . 1 + 4  = 0

p(1):1 + k - 3 + 4 = 0

p(1): k + 2 = 0

p(1): k = - 2

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{p(x) = x^3 + (k - 3)x^2 - x + 5}$

$\mathsf{p(1) = (1)^3 + (k - 3)(1)^2 - (1) + 5}$

$\mathsf{(1)^3 + (k - 3)(1)^2 - (1) + 5 = 0}$

$\mathsf{1 + (k - 3) - 1 + 5 = 0}$

$\mathsf{1 + (k - 3) - 1 + 5 = 0}$

$\mathsf{k - 3 + 5 = 0}$

$\mathsf{k + 2 = 0}$

$\boxed{\boxed{\mathsf{k = -2}}}$