SUMMARY
The equation x^2 + ax + b = 0 has roots x = -1 and x = 1. By factoring the equation as (x - 1)(x + 1) = 0 and expanding, it simplifies to x^2 - 1 = 0. This leads to the conclusion that the values of a and b are a = 0 and b = -1, confirming the solution is correct.
PREREQUISITES
- Understanding of quadratic equations
- Knowledge of factoring polynomials
- Familiarity with the concept of roots of equations
- Basic algebraic manipulation skills
NEXT STEPS
- Study the quadratic formula for solving equations
- Learn about the properties of polynomial roots
- Explore advanced factoring techniques in algebra
- Investigate the relationship between coefficients and roots in polynomial equations
USEFUL FOR
Students learning algebra, educators teaching quadratic equations, and anyone seeking to improve their problem-solving skills in mathematics.