Question

HELP, !Encontre as raízes da função quadrática 4x²-4x-3?

Answer 1

Eae mano,

na função

$f(x)=4x^2-4x-3$

fazemos f(x)=0..

$4x^2-4x-3=0\\\\ \begin{cases}a=4\\ b=-4\\ c=-3\end{cases}\\\\\\ \Delta=b^2-4ac\\ \Delta=(-4)^2-4\cdot4\cdot(-3)\\ \Delta=16+48\\ \Delta=64$ 

$x= \dfrac{-b\pm \sqrt{\Delta} }{2a}~\to~x= \dfrac{-(-4)\pm \sqrt{64} }{2\cdot4}~\to~x= \dfrac{4\pm8}{8} \\\\\\ \begin{cases}x'= \dfrac{4-8}{8}~\to~x'= -\dfrac{4}{8}~\to~x'= -\dfrac{1}{2}\\\\ x''= \dfrac{4+8}{8}~\to~x''= \dfrac{12}{8}~\to~x''= \dfrac{12\div4}{8\div4}~\to~x''= \dfrac{3}{2} \end{cases}$

Portanto, as raízes da função são..

$\Large\boxed{\boxed{x'= -\dfrac{1}{2}~~e~~x''= \dfrac{3}{2}}}$

Tenha ótimos estudos ;D