Resposta :
a) [tex]\text{x}^2-\text{x}-20=0[/tex]
[tex]\text{x}=\dfrax{-(-1)\pm\sqrt{(-1)^2-4\cdot1\cdot(-20)}}{2\cdot1}=\dfrac{1\pm9}{2}[/tex]
[tex]\text{x}'=\dfrac{1+9}{2}=5[/tex]
[tex]\text{x}"=\dfrac{1-9}{2}=-4[/tex]
b) [tex]\text{x}^2-3\text{x}-4=0[/tex]
[tex]\text{x}=\dfrac{-(-3)\pm\sqrt{((-3)^2-4\cdot1\cdot(-4)}}{2\cdot1}=\dfrac{3\pm5}{2}[/tex]
[tex]\text{x}'=\dfrac{3+5}{2}=4[/tex]
[tex]\text{x}"=\dfrac{3-5}{2}=-1[/tex]
c) [tex]\text{x}^2-8\text{x}+7=0[/tex]
[tex]\text{x}=\dfrac{-(-8)\pm\sqrt{(-8)^2-4\cdot1\cdot7}}{2\cdot1}=\dfrac{8\pm6}{2}[/tex]
[tex]\text{x}'=\dfrac{8+6}{2}=7[/tex]
[tex]\text{x}"=\dfrac{8-6}{2}=1[/tex]
d) [tex]5\text{x}^2-3\text{x}-2=0[/tex]
[tex]\text{x}=\dfrac{-(-3)\pm\sqrt{(-3)^2-4\cdot5\cdot(-2)}}{2\cdot5}=\dfrac{3\pm7}{10}[/tex]
[tex]\text{x}'=\dfrac{3+7}{10}=1[/tex]
[tex]\text{x}"=\dfrac{3-7}{10}=\dfrac{-4}{10}=\dfrac{-2}{5}[/tex]
a )x² - x - 20 =0
delta = (-1)^2 -4.1.(-20) = 1 + 80 = 81
x = 1 +/- V81 => 1 +/- 9 =>x1= 1+9 =>x1 = 5 ; x2= 1-9 =>x2 = - 4
2.1 2 2 2
b) x²-3x-4=0
delta = (-3)^2 -4.1.(-4) = 9 + 16 = 25
x = 3 +/- V25 => 3 +/- 5 =>x1= 3+5 =>x1 = 4 ; x2= 3-5 =>x2 = - 1
2.1 2 2 2
c) x²-8x+7=0
delta = (-8)^2 -4.1.7 = 64- 28 = 36
x = 8 +/- V36 => 8 +/- 6 =>x1= 8+6 =>x1 = 7 ; x2= 8-6 =>x2 = 1
2.1 2 2 2
d) 5x²-3x -2 =0
delta = (-3)^2 -4.5.(-2) = 9 + 40 = 49
x = 3 +/- V49 => 3 +/- 7 =>x1= 3+7 =>x1 = 1 ; x2= 3-7 => x2 = - 4
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