. What are the exact solutions of x2 - x - 4 = 0?
2 answers:
X ² - x - 4 = 0
![x_{1} = \frac{1+ \sqrt{1+16} }{2}= \frac{1+ \sqrt{17} }{2} = 2.56](https://tex.z-dn.net/?f=%20%20x_%7B1%7D%20%20%3D%20%5Cfrac%7B1%2B%20%5Csqrt%7B1%2B16%7D%20%20%7D%7B2%7D%3D%20%5Cfrac%7B1%2B%20%5Csqrt%7B17%7D%20%7D%7B2%7D%20%3D%202.56%20)
![x_{2} = \frac{1- \sqrt{17} }{2}= - 1.56](https://tex.z-dn.net/?f=%20x_%7B2%7D%20%3D%20%20%5Cfrac%7B1-%20%5Csqrt%7B17%7D%20%7D%7B2%7D%3D%20-%201.56%20%20)
Exact values are
x 1 = 2.56 and x 2 =
-1.56
Answer:
and ![x=\frac{1-\sqrt{17}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1-%5Csqrt%7B17%7D%7D%7B2%7D)
Step-by-step explanation:
![x^2 - x - 4 = 0](https://tex.z-dn.net/?f=x%5E2%20-%20x%20-%204%20%3D%200)
To solve for x , apply quadratic formula
![x=\frac{-b+-\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
a=1 , b= -1 , c= -4
Plug in all the values in the formula
![x=\frac{-(-1)+-\sqrt{(-1)^2-4(1)(-4)}}{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-1%29%2B-%5Csqrt%7B%28-1%29%5E2-4%281%29%28-4%29%7D%7D%7B2%281%29%7D)
![x=\frac{1+-\sqrt{1+16}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%2B-%5Csqrt%7B1%2B16%7D%7D%7B2%7D)
![x=\frac{1+-\sqrt{17}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%2B-%5Csqrt%7B17%7D%7D%7B2%7D)
and ![x=\frac{1-\sqrt{17}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1-%5Csqrt%7B17%7D%7D%7B2%7D)
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Answer:
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Step-by-step explanation:
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Step-by-step explanation: