Advanced Algebraic Equations

1. ax + b = 0.   Linear (algebraic) equation.
   
2. ax² + bx + c = 0.   Quadratic equation.
   
3. ax³ + bx² + cx + d = 0.   Cubic equation.
   
4. ax⁴ + bx² + c = 0.   Biquadratic equation.
   
5. ax⁴ + bx³ + cx² + bx + a = 0.   Reciprocal (algebraic) equation.
   
6. ax⁴ + bx³ + cx² − bx + a = 0.   Modified reciprocal equation.
   
7. ab²x⁴ + bx³ + cx² + dx + ad² = 0.   Generalized reciprocal equation.
   
8. ax⁴ + bx³ + cx² + dx + e = 0.   Quartic equation of general form.
   
9. xⁿ − a = 0.   Binomial algebraic equation of degree n.
   
10. ax²ⁿ + bxⁿ + c = 0.
    
11. a₀x²ⁿ + a₁x²ⁿ⁻¹ + a₂x²ⁿ⁻² + ... + a₂x² + a₁x + a₀ = 0.   Reciprocal (algebraic) equation.
    
12. a_nxⁿ + a_n−1xⁿ⁻¹ + ... + a₁x + a₀ = 0.   Algebraic equation of general form of degree n.