We will solve an extreme quintic equation x^5-5x+3=0 by brute force factoring. This is a solvable quintic because we can factor the quintic expression = quadratic * cubic by using the undetermined coefficients method. Then we can use the quadratic formula to solve the quadratic equation (and we will get a negative golden ratio). For the cubic, I will not use the cubic formula but I will show you the Lagrange Resolvent approach and we can find its real solution. Let me know if you can find the complex solutions to the cubic equation.

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Try another famous extreme algebra problem 👉    • Extreme Algebra Question  (#patience)  
Solve this quintic equation by Newton's method 👉    • Newton's method (introduction & example)  
Another equation by the Lagrange Resolvent 👉    • solving a cubic equation by completin...  
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