Page 3: Completing the Solution
This final page focuses on solving the remaining quadratic equation to find all roots of the polynomial.
After factoring out x−1, we're left with the quadratic equation x^2 - 5x + 4 = 0.
Vocabulary: The quadratic formula is used to solve equations in the form ax^2 + bx + c = 0, where a ≠ 0.
Steps to solve the quadratic equation:
- Calculate the discriminant: Δ = b^2 - 4ac = 25 - 16 = 9
- Apply the quadratic formula: x = −b±√Δ / 2a
Example: x1 = 5+√9 / 2 = 4, x2 = 5−√9 / 2 = 1
The solution verifies our earlier findings that x = 1 and x = 4 are the only roots of the polynomial.
Highlight: This method demonstrates how to find pierwiastki wymierne wielomianu rationalrootsofpolynomials by combining factoring and the quadratic formula.
This comprehensive approach showcases the Twierdzenie o pierwiastkach wymiernych TheoremonRationalRoots in action, providing a thorough understanding of how to wyznacz pierwiastki wielomianu in various scenarios.