Question

Calcule as raízes, caso existam, da seguinte função quadrática f(x) = x²+3x+2

Answer 1

As raízes da função são os valores de x que tornam f(x)=0

Portanto

$\mathsf{x^2+3x+2=0}\\\mathsf{a=1~~~b=3~~~c=2}\\\mathsf{\Delta=b^2-4ac}\\\mathsf{\Delta=3^2-4.1.2}\\\mathsf{\Delta=9-8}\\\mathsf{\Delta=1}\\\mathsf{x=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\mathsf{x=\dfrac{-3\pm\sqrt{1}}{2.1}}\\\mathsf{x=\dfrac{-3\pm1}{2}}\implies\begin{cases}\mathsf{x_{1}=\dfrac{-3+1}{2}=-\dfrac{2}{2}=-1}\\\mathsf{x_{2}=\dfrac{-3-1}{2}=-\dfrac{4}{2}=-2}\end{cases}$