Question

fatore e resolva a equações a seguir :a)x elevado 2 -4x-21=0

Answer 1

Resolução pela fórmula de Bhaskara, veja:

$x^{2}-4x-21=0\\\\\\ x = -b~+_{-}~\dfrac{\sqrt{b^{2}-4~.~a~.~c}}{2~.~a}}\\\\\ x = 4~+_{-}~\dfrac{ \sqrt{(-4)^{2}-4~.~1~.~(-21)}}{2~.~1}}\\\\\ x = 4~+_{-}~\dfrac{ \sqrt{16+84}}{2}}\\\\\ x = 4~+_{-}~\dfrac{ \sqrt{100}}{2}}\\\\\ x = 4~+_{-}~\dfrac{10}{2}\\\\\ x' = \dfrac{4 + 10}{2}\\\\\ x' = \dfrac{14}{2} =\ \textgreater \ \large\boxed{\boxed{x' = 7.}}}\\\\\\ x'' = \dfrac{4-10}{2}\\\\ x'' = \dfrac{-6}{2}} =\ \textgreater \ \large\boxed{\boxed{x''=-3.}}\\\\\\ \large\boxed{\boxed{x'=7~e~x''=-3.}}$

Espero que te ajude :).

Answer 2

x² - 4x - 21 = 0

x(x - 4) - 21 = 0
(x - 7).(x + 3)  => forma fatorada da equação;

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Pra encontrar as raízes igualar os termo a zero:

x - 7 = 0
x' = 7

x + 3 = 0
x'' = -3

Raízes da equação: 

S = {7, -3}