Equação do 2° Grau (Segundo Grau) - Matemática Básica

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Ensino Fundamental | Ensino Médio | Matemática Financeira
Equação do 2° Grau (Segundo
Grau)
Ensino Fundamental > Equação do 2° Grau (Segundo Grau)
Atualizado: 30/05/2018
Uma equação do 2° grau é uma equação que tem duas incógnita x,
sendo que uma delas possuem um grau igual a 2.
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Exemplo:
2x² + 5x + 3 = 0 (essa é uma equação do segundo grau, veja o
grau 2 na primeira incógnita)
Toda equação do 2° grau tem a seguinte forma:
ax² + bx + c = 0, onde a, b, c ∈ R e com a ≠ 0.
Chamamos a, b e c de coeficientes, a é sempre coeficiente de x², b é
sempre coeficiente de x e c é sempre coeficiente do termo
independente.
Exemplo:
3x² + 4x + 1 = 0 é uma equação do segundo grau, com a = 3, b =
4, c = 1.
x² – x – 1 = 0 é uma equação do segundo grau, com a = 1, b = –
1, c = –1 .
9x² – 5x = 0 é uma equação do segundo grau, com a = 9, b = –5,
c = 0.
5x² –4 = 0 é uma equação do segundo grau, com a = 5, b = 0, c
= –4.
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Equação do 2° grau completa
e incompleta
Uma equação do 2° é chamada completa quando os coeficientes b e
c são diferentes de zero.
Exemplos:
2x² + 3x + 3 = 0
x² + x + 1 = 0
São equações completas.
Uma equação do 2° grau é chamada incompleta quando os
coeficientes b ou c é igual a zero, basta um deles ser igual a zero, ou
ambos serem iguais a zero.
Exemplos:
x² – 3 = 0 (b = 0)
2x² + x = 0 (c = 0)
5x² = 0 (b = 0 e c = 0)
Raízes de uma equação do 2°
grau
Reforço Escolar - Prof. Irineu Shimabukuro
Matemática-Física-Química-Cálculo-Lógica/Fundamental/Médio/ Vestibular/Concursos
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Para resolvermos uma equação do 2° grau é necessário que
encontremos as raízes da equação. As raízes são valores que
quando substituímos nas incógnitas torna a sentença verdadeira.
Assim, as raízes da equação forma o conjunto solução ou o conjunto
verdade da equação.
Fórmula de Bhaskara
A fórmula de Bhaskara é o método mais fácil para encontrarmos as
raízes da equação.
Exercício resolvido de uma
equação do 2° grau
Encontre a solução para a seguinte equação: x² – 5x + 6 = 0
Resposta:
Primeiro vamos encontrar os coeficientes da equação, isto é, os
valores de a, b e c.
a = 1 b = –5 c = 6
Agora, vamos aplicar a fórmula de Bhaskara, substituindo os valores
correspondentesaos coeficientes a, b e c, para encontramos as
raízes da equação:
(–(–5)) = 5 e (–5)² = (–5) x (–5) = 25 (menos com menos é mais,
estude potenciação)
Vamos separar a equação pois temos que analisar separados, ou
seja, quando verificarmos para + chamaremos de x1 e quando
verificarmos para – chamaremos de x2. Veja:
https://matematicabasica.net/potenciacao/
Então, agora encontramos as raízes da equação: x1 = 3 e x2 = 2
Estas são as raízes da equação, ou seja, o conjunto solução que
resolve a equação. Que torna ela verdadeira.
S = {2, 3}
Veja:
Se substituirmos as raízes veremos que elas realmente resolvem a
equação.
Leia também
Equação do 1° grau
“
https://matematicabasica.net/equacao-do-1-grau-primeiro-grau/
 
 
 
 
Autor
 by Jean Carlos Novaes
Formado em Ciência da Computação na UFBA. Depois de ficar sete anos tentando
cursar uma universidade, conseguiu entrar na UFBA prestando um dos mais
concorridos vestibulares do país. 
LinkedIn
Veja também
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Harley Suzart • um ano atrás
Para saber o x1 e x2 de uma equação do segundo grau onde o A= a 1 ex x² – 5x + 6 = 
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 • Responder •
um macete: sempre procurar a "soma do produto" como assim? simples só descobrir q
soma da o valor de b e na multiplicação dê o valor de c. na pratica 2+3=5 2.3=6 pode v
resposta final foi {2,3}. 
mas tem uma regrinha, no caso do 5 na equação ele está negativo, para fazer essa jog
ele deve ser positivo, se ele estivesse positivo, deveria ficar negativo 
outra equação: x²-9x-10=0, no caso seria 1 e -9 que na multiplicação da 9 e somando d
3△ ▽
 • Responder •
Alessandra • 3 meses atrás> Harley Suzart
Como monta a equação do 2 grau
△ ▽
 • Responder •
Luis Antonio Strengari Nanci F • 8 meses atrás> Harley Suzart
Na verdade deve-se encontrar dois números que somados sejam igual à soma d
que multiplicados sejam igual à c.
△ ▽
 • Responder •
Luciene Silveira • um ano atrás> Harley Suzart
Resolvi sua equação x²-9x-10=0 e meu resultado foi: x1= -1 e x2=10
△ ▽
 • Responder •
LENDÁRIO hard games • 10 meses atrás> Luciene Silveira
erro feio amiga resultado:46 and 35
1△ ▽
 • Responder •
Roberta Goes da Silva • 2 meses atrás> LENDÁRIO hard games
o sem em que esta errado o resultado da luciene esta correto
△ ▽
 • Responder •
Genoh Silva • 2 meses atrás> Luciene Silveira
O meu também deu esse resultado.
△ ▽
 • Responder •
Júlio Ronqui • 6 meses atrás> Luciene Silveira
TAMBÉM RESOLVI E O RESULTADO FOI O MESMO !
△ ▽
 • Responder •
Pamela Oliver • um ano atrás> Harley Suzart
Interessante, mas e se em algum momento der errado?
△ ▽
 • Responder •
Diogo Marinho • um ano atrás> Pamela Oliver
É um ótimo macete, porém somente quando (a = 1). Se ( a # 1), é precis
utilizar um outro macete. 
Pamela Oliver, como disse anteriormente, esse macete faz parte da ciên
exata. Rs Não tem como dar errado, basta apenas que verifique a condiç
(a).
△ ▽
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 • Responder •
kimimaru_kaguya • um ano atrás> Diogo Marinho
Não tem como dá errado? Então pq deu!! No segundo exemplo q
deu os resultados deu tudo errado não são 1 e -9 e sim 10 e -1
△ ▽
 • Responder •
Genoh Silva • 2 meses atrás> kimimaru_kaguya
Meu resultado também deu 10 e -1
△ ▽
 • Responder •
Adriano Matias • 9 meses atrás> kimimaru_kaguya
não deu errado. Ele que errou.
△ ▽
 • Responder •
Legend 07 • 8 meses atrás> Adriano Matias
kkkkkk vdd
△ ▽
 • Responder •
Leno Sanoli • 10 meses atrás
A fórmula inicial esta errada, o 2.a deve ficar fora da raiz.
o correto é: 
⛺
4△ ▽
 • Responder •
Jean Carlos Novaes • 10 meses atrásModerador > Leno Sanoli
Corrigido!
3△ ▽
 • Responder •
Aparecida Maria De Jesus • 5 meses atrás> Jean Carlos Novaes
to apanhando nessa equacao do segundo grau k
1△ ▽
 • Responder •
Iae Daniel Mourao Imvu Imvu • 5 meses atrás
Eu to no ensino medio e nao sei nada de matematica meu deus
1△ ▽
 • Responder •
Giovanni Fois • 10 meses atrás
ao determinar os coeficientes da equação, temos b=-5. Em seguida na fórmula o valor d
aparece como -5 quando o correto seria -(-5) = +5. Precisa corrigir (fórmula logo acima 
frase "menos com menos dá mais, estude potenciação")!
1△ ▽
• Responder •
Jean Carlos Novaes • 10 meses atrásModerador > Giovanni Fois
Feito. =)
△ ▽
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 • Responder •△ ▽
 • Responder •
Wera Brito • um ano atrás
ótima explicação, adorei
1△ ▽
 • Responder •
Carlos Matheus • um ano atrás
oche doido q massa
1△ ▽
 • Responder •
Solange Endo • um ano atrás
Excelente explicação!!! Parabéns!
1△ ▽
 • Responder •
Dooh Pantoja Dos Santos • um ano atrás
obg <3 aprendii ! mtt
1△ ▽
 • Responder •
Lucas Lopasso • um ano atrás> Dooh Pantoja Dos Santos
Muito bom né ? Melhor explicação rsrs <3
1△ ▽
 • Responder •
saviio striiley • 3 meses atrás
PARA SABER SE O 0 E CORRESPONDIDO PELA RAIZ QUADRADA E NECESSARIO
SABER QUE VALOR DO RESULTADO E PRECISO ALCANÇAR O OBJETIVO DA MAT
DA ECOLOGIA HUMANA E DESUMANA DE VARIAS RAIZES AO QUADRADO E FEIT
ESPAÇO DO UNIVERSO DA GALAXIA DO ESPAÇO E FILOSOFIA TERRESTRE E
ALIENÍGENA ENTAO COM TODAS ESSAS INFORMAÇOES SABEMOS QUE TODA A
MATERIA E VIVA E TODA MATERIA TBM NAO E VIVA
△ ▽
 • Responder •
jUBISITUDEKO • 4 meses atrás
nacanduvar fanisti
△ ▽
 • Responder •
jUBISITUDEKO • 4 meses atrás
arroz doce 
e melhor que açafrao seu espinafre do prof rabanete degustado ao molho madeira com
pepitos de pepinos com aspargos fatiados com ervilhas recheada de leite de coco refin
△ ▽
 • Responder •
jUBISITUDEKO • 4 meses atrás
Aeeeeeeee o tcholaaaaaaaaaaaaaaaa
△ ▽
 • Responder •
rose • 4 meses atrás
Preciso pagar 52% de uma divida de R$ 15.200,00.Qual o valor do meu pagamento?
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 • Responder •
Nina Al • 3 meses atrás> rose
Rose, para fazer percentual basta multiplicar. Ou seja: 15.200,00 x 52% = 7.904
△ ▽
 • Responder •
Thaís Fontenele • 4 meses atrás> rose
R$7.904, é o que vc deve pagar.
△ ▽
 • Responder •
Guilherme Roberto • 5 meses atrás
pow imagina com toda essa matemática, toda essa ciência e tecnologia podemos criar 
acelerador de particulas da série de televisão: The Flash
△ ▽
 • Responder •
Ryan • 2 meses atrás> Guilherme Roberto
Já existe vários aceleradores de partículas
△ ▽
 • Responder •
Aparecida Maria De Jesus • 5 meses atrás
como somar x-10x+9=0
△ ▽
 • Responder •
João Paulo • 3 meses atrás> Aparecida Maria De Jesus
X -10x +9 = 0 (passa o 9 pro outro lado da igualdade como -9 ) 
X -10x = -9 ( subtrair os termos iguais, lembre x vale 1 ou seja, 1x - 10x) 
-9x = -9 (agora o -9 que está com o X, vai passar dividindo) 
( MENOS COM MENOS DÁ MAIS +, ENTÃO...)
X= 9/9 (NOVE DIVIDIDO POR 9) OU SEJA, x=1
△ ▽
 • Responder •
Vitoria Park • 6 meses atrás
Que equação maravilhosona bicho😊
△ ▽
 • Responder •
Kayo Victor • 6 meses atrás
não entendi pq o 24 ? de onde ele veio
△ ▽
 • Responder •
Gilvan Lima • 6 meses atrás> Kayo Victor
multiplicando 4x1x6= 24
△ ▽
 • Responder •
Laura Nisimura • 6 meses atrás
parabéns otimo ensino esta me ajudando a me preparar para a prova do etec 2018
△ ▽
Rafael Volner • 8 meses atrás
-5² da -25. 
Mas acredito que a intenção era escrever ( 5)²
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 • Responder •
Mas acredito que a intenção era escrever (-5)²
△ ▽
 • Responder •
Rafael Volner • 8 meses atrás> Rafael Volner
3x esse erro ocorre. 
E no final, quando substitui as raízes, o "-5" tmb deveria estar entre parenteses 
△ ▽
 • Responder •
Adriano Matias • 9 meses atrás
Isso é uma regra bem utiliza. Se chama a regra da soma S e do produto P. 
Dois números que multiplicados dê P= c/a. e somado de S= - b/a. Sempre quando a=1.
fiquem atentos com o sinal, pois ele inverte.
Então na equação x²-9x-10=0, a nossa amiga acertou. 
dois números que multiplicado dê 10 e somado dê -9. so pode ser X1= -1 e X2 = 10.
△ ▽
 • Responder •
Jean Inútilys • 10 meses atrás
Porque o -5 elevado a 2 ficou positivo (25)?
△ ▽
 • Responder •
pedro bezerra • 10 meses atrás> Jean Inútilys
pq (-5)² = (-5) * (-5) 
dai você multiplica o 5*5 = 25 >>>>>>>>>>>> ai você terá (+25) 
e multiplica tbm o sinal (-) * (-) = (+)
2△ ▽
 • Responder •
Jonas salles • 8 meses atrás> Jean Inútilys
N elevados a exp par fica positivo 
N elevado a exp impar fica negativo
△ ▽
 • Responder •
Namikaze TV • um ano atrás
par que usar formula de baskara 
faiz noraml vei
△ ▽
 • Responder •
LENDÁRIO hard games • 10 meses atrás> Namikaze TV
n da veio é isso ou nada
△ ▽
 • Responder •
Claudio Lopes Dias • 10 meses atrás> Namikaze TV
como fazer normal
△ ▽
 • Responder •
Master Hater • um ano atrás
estou aprendendo agora não entendi nada isto esta muito complicado
△ ▽
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