As equações seguintes estão escritas na forma reduzida. Calcule o discriminante Δ de cada uma e identifique o tipo de rais que cada equação apresenta. a) x²+8x+20=0 b) x²+6x-4=0 c)5x²-3x+1=0 d) 6x²-x-1=0 e)-x²+10x-16=0Por favor me ajudem preciso entregar essa questão pra amanhã.. Socorro :(
Soluções para a tarefa
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42
a)
Δ = b² - 4ac
Δ = 8² - 4*1*20
Δ = 64 - 80
Δ = -16
Δ < 0, não existe raiz de número negativo. S = {∅}
b) x² + 6x -4 = 0
Δ = b² - 4ac
Δ = 6² - 4*1*(-4)
Δ = 36 + 16
Δ = 52
52 não é quadrado perfeito, portanto não há solução exata.
c) 5x² -3x +1 = 0
Δ = (-3)² - 4*5*1
Δ = 9 - 20
Δ = -11
Δ < 0, não existe raiz de número negativo.
d) 6x² -x -1 = 0
Δ = (-1)² - 4*6*(-1)
Δ = 1 + 24
Δ = 25 (Δ > 0, possui duas raízes distintas)
x' = 1/2; x'' = -1/3
e) -x² + 10x - 16 = 0
Δ = 10² - 4*(-1)*(-16)
Δ = 100 - 64
Δ = 36
Δ > 0, possui duas raízes distintas
x' = 2, x'' = 8
Δ = b² - 4ac
Δ = 8² - 4*1*20
Δ = 64 - 80
Δ = -16
Δ < 0, não existe raiz de número negativo. S = {∅}
b) x² + 6x -4 = 0
Δ = b² - 4ac
Δ = 6² - 4*1*(-4)
Δ = 36 + 16
Δ = 52
52 não é quadrado perfeito, portanto não há solução exata.
c) 5x² -3x +1 = 0
Δ = (-3)² - 4*5*1
Δ = 9 - 20
Δ = -11
Δ < 0, não existe raiz de número negativo.
d) 6x² -x -1 = 0
Δ = (-1)² - 4*6*(-1)
Δ = 1 + 24
Δ = 25 (Δ > 0, possui duas raízes distintas)
x' = 1/2; x'' = -1/3
e) -x² + 10x - 16 = 0
Δ = 10² - 4*(-1)*(-16)
Δ = 100 - 64
Δ = 36
Δ > 0, possui duas raízes distintas
x' = 2, x'' = 8
Respondido por
2
Bom dia!
Solução!
Para esse tipo de descriminante temos duas soluções:reais ou complexos,complexo quando o delta for menor que zero.\\\\\\\\\\\\\![\boxed{\Delta=b^{2}-4\timesa \times c} \\\\\\\\\
Se!](https://tex.z-dn.net/?f=%5Cboxed%7B%5CDelta%3Db%5E%7B2%7D-4%5Ctimesa+%5Ctimes+c%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%0ASe%21+ "\boxed{\Delta=b^{2}-4\timesa \times c} \\\\\\\\\
Se!")
![\Delta=b^{2}-4\timesa \times c\\\\\\\\
x^{2} +8x+20=0\\\\\\\\\
\Delta=8^{2}-4\times1 \times 20\\\\\\\
\Delta=64-80\\\\\\\
\Delta=-16\\\\\\\
\Delta \ \textless \ 0 \in\mathbb{C}\\\\\\\\\\\
x^{2} +6x+4=0\\\\\\\\
\Delta=6^{2}-4\times1 \times 4\\\\\\\\
\Delta=36-16\\\\\\\\
\Delta=20\\\\\\\\
\Delta \ \textgreater \ 0 \in\mathbb{R}](https://tex.z-dn.net/?f=%5CDelta%3Db%5E%7B2%7D-4%5Ctimesa+%5Ctimes+c%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A+x%5E%7B2%7D+%2B8x%2B20%3D0%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D8%5E%7B2%7D-4%5Ctimes1+%5Ctimes+20%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D64-80%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D-16%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta+%5C+%5Ctextless+%5C+0+%5Cin%5Cmathbb%7BC%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A+x%5E%7B2%7D+%2B6x%2B4%3D0%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D6%5E%7B2%7D-4%5Ctimes1+%5Ctimes+4%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D36-16%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D20%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta+%5C+%5Ctextgreater+%5C+0+%5Cin%5Cmathbb%7BR%7D+ "\Delta=b^{2}-4\timesa \times c\\\\\\\\
x^{2} +8x+20=0\\\\\\\\\
\Delta=8^{2}-4\times1 \times 20\\\\\\\
\Delta=64-80\\\\\\\
\Delta=-16\\\\\\\
\Delta \ \textless \ 0 \in\mathbb{C}\\\\\\\\\\\
x^{2} +6x+4=0\\\\\\\\
\Delta=6^{2}-4\times1 \times 4\\\\\\\\
\Delta=36-16\\\\\\\\
\Delta=20\\\\\\\\
\Delta \ \textgreater \ 0 \in\mathbb{R}")
![6 x^{2} -x-1=0\\\\\\\
\Delta=(-1)^{2}-4\times6 \times-1\\\\\\\\
\Delta=1+24\\\\\\\\
\Delta=25\\\\\\\\
\Delta \ \textgreater \ 0 \in\mathbb{R}\\\\\\\\\\\\
- x^{2} +10x-16=0\\\\\\\
\Delta=10^{2}-4\times-1 \times -16\\\\\\\\
\Delta=100-64\\\\\\\\
\Delta=100-64\\\\\\\\
\Delta=36\\\\\\\\
\Delta \ \textgreater \ 0 \in\mathbb{R}](https://tex.z-dn.net/?f=6+x%5E%7B2%7D+-x-1%3D0%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D%28-1%29%5E%7B2%7D-4%5Ctimes6+%5Ctimes-1%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D1%2B24%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D25%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta+%5C+%5Ctextgreater+%5C+0+%5Cin%5Cmathbb%7BR%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A-+x%5E%7B2%7D+%2B10x-16%3D0%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D10%5E%7B2%7D-4%5Ctimes-1+%5Ctimes+-16%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D100-64%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D100-64%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta%3D36%5C%5C%5C%5C%5C%5C%5C%5C%0A%5CDelta+%5C+%5Ctextgreater+%5C+0+%5Cin%5Cmathbb%7BR%7D+%0A "6 x^{2} -x-1=0\\\\\\\
\Delta=(-1)^{2}-4\times6 \times-1\\\\\\\\
\Delta=1+24\\\\\\\\
\Delta=25\\\\\\\\
\Delta \ \textgreater \ 0 \in\mathbb{R}\\\\\\\\\\\\
- x^{2} +10x-16=0\\\\\\\
\Delta=10^{2}-4\times-1 \times -16\\\\\\\\
\Delta=100-64\\\\\\\\
\Delta=100-64\\\\\\\\
\Delta=36\\\\\\\\
\Delta \ \textgreater \ 0 \in\mathbb{R}")
Bom dia!
Bons estudos!
Solução!
Para esse tipo de descriminante temos duas soluções:reais ou complexos,complexo quando o delta for menor que zero.\\\\\\\\\\\\\
Bom dia!
Bons estudos!
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