Question

A equação do segundo grau cujas raizes são -1/2 e 1/3 é:

a) x^2 - 1/2x + 1/3=0
b) x^2 + 1/2x + 1/3 =0
c) 6x^2 + x - 1 =0
d) 6x^2 - x + 1 =0

PRECISO URGENTE..

Answer 1

$\boxed{\begin{array}{l}\underline{\sf Equac_{\!\!,}\tilde ao\,de\,2^o\,grau}\\\underline{\sf em\,func_{\!\!,}\tilde ao\,da\,soma~s~e~do~produto~p}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x^2-sx+p=0}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\sf s=-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{-3+2}{6}=-\dfrac{1}{6}\\\\\sf p=\bigg(-\dfrac{1}{2}\bigg)\cdot\dfrac{1}{3}=-\dfrac{1}{6}\\\\\sf x^2-\bigg(-\dfrac{1}{6}\bigg)x+\bigg(-\dfrac{1}{6}\bigg)=0\\\\\sf x^2+\dfrac{1}{6}x-\dfrac{1}{6}=0\bullet 6\\\sf 6x^2+x-1=0\\\huge\boxed{\boxed{\boxed{\boxed{\rm\blue{\maltese}~\red{alternativa~c}}}}}\end{array}}$