Question

UFRGS-RS As raizes do polinômio p(x) = x^3 +5x^2 +4x são :

Answer 1

Resposta:

x = 0 ou x=-1 ou x=-4

Explicação passo-a-passo:

$x^3 +5x^2 + 4x = 0\\x(x^2 + 5x + 4) = 0\\x = 0 \\ ou \\ x^2 + 5x + 4 =0$

Δ = $(5)^2 - 4(1)(4)=9\\x_1=\frac{-5 + \sqrt{9} }{2} = \frac{-5+3}{2}=\frac{-2}{2} = -1  \\x_2=\frac{-5 - \sqrt{9} }{2} = \frac{-5-3}{2} = \frac{-8}{2} = -4$

Answer 2

Resposta:

${x}^{3} + 5 {x}^{2} + 4x \\ x( {x }^{2} + 5x + 4) \\ x( {x}^{2} + 4x + x + 4) \\ x(x + 4)(x + 1).$