Question

Escreva uma equação do 2º grau cujas raízes sejam:
a)x₁ = 3 e x₂ = 4
S = x₁ + x₂ = 3 + 4 = 7
P = x₁ . x₂ = 3 . 4 = 12
x² - Sx + P = 0
x² - 7x + 12 = 0 (possível resposta)
b)x₁ = -5 e x₂ = 7




c)x₁ = 1 e x₂ = -6
ME AJUDEM A RESOLVER AS DUAS ULTIMAS

Answer 1

a)

$\mathsf{x_{1}=3~~x_{2}=4}\\\mathsf{s=x_{1}+x_{2}=3+4=7} \\ \mathsf{p=x_{1}.x_{2}=3.4=12}\\\mathsf{x^{2}-sx+p=0}\\\mathsf{x^{2}-7x+12=0}$

b)

$\mathsf{x_{1}=-5~~x_{2}=7}\\\mathsf{s=x_{1}+x_{2}=-5+7=2} \\ \mathsf{p=x_{1}.x_{2}=(-5).7=-35}\\\mathsf{x^{2}-sx+p=0}\\\mathsf{x^{2}-2x-35=0}$

c)

$\mathsf{x_{1}=1~~x_{2}=-6}\\\mathsf{s=x_{1}+x_{2}=1-6=-5} \\ \mathsf{p=x_{1}.x_{2}=1.(-6)=-6}\\\mathsf{x^{2}-sx+p=0}\\\mathsf{x^{2}+5x-6=0}$