Question

Quais as raizes das equações:

a) x^2-121=0

b)-x^2+4x+12=0

Answer 1

Resposta:

a)

x²-121=0

x²=121

x=±√121

x=±11

S={-11, 11}

b)

-x²+4x+12=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~-1x^{2}+4x+12=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=-1{;}~b=4~e~c=12\\\\\Delta=(b)^{2}-4(a)(c)=(4)^{2}-4(-1)(12)=16-(-48)=64\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(4)-\sqrt{64}}{2(-1)}=\frac{-4-8}{-2}=\frac{-12}{-2}=6\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(4)+\sqrt{64}}{2(-1)}=\frac{-4+8}{-2}=\frac{4}{-2}=-2\\\\S=\{6,~-2\}$

Answer 2

A) x² - 121 = 0

x²= 0 + 121

x²= 121

x=± √121

x= ± 11

S= ( 11 , - 11)

B) - x² + 4x + 12 = 0

A= - 1

B= 4

C= 12

∆= b² - 4ac

∆= 4² - 4 • ( - 1) • 12

∆= 16 + 48

∆= 64

x= - b ± √∆ / 2a

x= - 4 ± √64 / 2 • ( - 1)

x'= - 4 + 8/-2 = 4/-2 = - 2

x''= - 4 - 8/-2 = - 12/-2 = 6

S= ( - 2 , 6)