Question

forma fatorada de equacao x² - 3x -10= 0

Answer 1

A forma fatorada é dada na forma:

$a.(x-x').(x-x'')~=~0\\\\Onde~"a"~\acute{e}~o~coeficiente~que~multiplica~x^2~e~x'~e~x''~as~raizes$

Sendo assim, vamos achar as raízes da equação por Bhaskara:

$\Delta~=~(-3)^2-4.1.(-10)~=~9+40~=~\boxed{49}\\\\\\x'~=~\frac{3+\sqrt{49}}{2~.~1}~=~\frac{3+7}{2}~=~\frac{10}{2}~~\rightarrow~\boxed{x'=5}\\\\\\x''~=~\frac{3-\sqrt{49}}{2~.~1}~=~\frac{3-7}{2}~=~\frac{-4}{2}~~\rightarrow~\boxed{x''=-2}$

Substituindo no modelo:

$a.(x-x').(x-x'')~=~0\\\\\\1.(x-5).(x-(-4))~=~0\\\\\\\boxed{(x-5).(x+4)~=~0}$