Question

Resolve as equações incompletas, identifica o termo que está faltando (termo B ou termo C), utilizando a fórmula acha os valores das incógnitas.

a) 3x2 – 9x=0
b) 10x2 – 1000 = 0
c) 4x2 - 25 = 11
d) 7x2 +2= 30
e) – 4x2 – 8x =0

Answer 1

Resposta:

$a)~~3x^{2} -9x=0~~~~coeficientes:a=3,~b=-9,~c=0\\ \\ 3x(x-3)=0\\ \\ 3x=0\\ \\ x'=\frac{0}{3} =0\\ \\ x-3=0\\ \\ x''=3~~~~~~~~~~~~S\left \{ {{0,~3} {}} \}$

$b)~~10x^{2} -1000=0~~~~coeficientes:a=10,~b=0,~c=1000\\ \\ x=\sqrt{\frac{-c}{a} } \\ \\ x=\sqrt{\frac{-(-1000}{10} } \\ \\ x=\sqrt{100}\\ \\ x'=10\\ \\ x''=-10~~~~~~~~~~~~S~~\left \{ {{-10,~10} {}} \}$

$c)~~4x^{2} -25=11\\ \\ 4x^{2} -25+11=0\\ \\ 4x^{2} -14=0~~~~coeficientes:a=4,~b=0,~c=-14\\ \\ x=\sqrt{\frac{-c}{a} } \\ \\ x=\sqrt{\frac{-(-14)}{4} } =\sqrt{\frac{14}{4} } =\sqrt{\frac{7}{2} } \\ \\ x'=-\sqrt{\frac{7}{2} } \\ \\ x''=\sqrt{\frac{7}{2} } ~~~~~~~~S~~\left \{ {{-\sqrt{\frac{7}{2} },~~\sqrt{\frac{7}{2} } } {}} \}$

$d)~~7x^{2} +2=30\\ \\ 7x^{2} +2-30=0\\ \\ 7x^{2} -28=0~~coeficientes:~a=7,~b=0,~c=-28\\ \\ x=\sqrt{\frac{-c}{a} } \\ \\ x=\sqrt{(\frac{-(-28)}{7} } =\sqrt{\frac{28}{7} } =\sqrt{4} \\ \\ x'=-2\\ \\ x''=2~~~~~~~~~~~~S~~\left \{ {{-2,~2} {}} \}$

$e)~~-4x^{2} -8x=0~~~~coeficientes:a=-4,~b=-8,~c=0\\ \\ 4x(-x-2)=0\\ \\ 4x=0\\ \\ x'=\frac{0}{4} =0\\ \\ -x-2=0\\ \\ -x=2\\ \\ x''=-2~~~~~~~~~~S~~\left \{ {{0,~-2} {}} \}$