Question

Encontre Os Valores Reais De Z tais que:

a.Z² - 7z = 0

b.2 z² - 16 z = 20

c. 5 z²+ 20 z = 0
d.-2 z² - 42 z = 0

Answer 1

A)
$z^{2}=7z \\ \frac{z^{2}}{z} = \frac{7z}{z} \\ z=7$
B)
$2z^{2}-16z-20=0$ eq. do segundo grau - Resolver pela forma de Bascara
$z= \frac{-b+ \sqrt{b^{2}-4ac}}{2a}$$\frac{-(-16)+ \sqrt{(-16)^{2}-4(2)(-20)}}{2(2)} \\ \frac{16+ \sqrt{416}}{4} \\ z_{1} = -1,099 \\ z_{2}=9,099$
C)
$5z^{2}=-20z \\ \frac{5z^{2}}{z} = \frac{-20z}{z} \\ z=\frac{-20}{5} \\ z=-4$
D)
$-2z^{2}=42z \\ \frac{2z^{2}}{z} = \frac{-42z}{z} \\ 2z=-42 \\ z= \frac{-42}{2} \\ z=-21$