Quadratic Formula
一元二次方程求根公式
Theoretical Identity Description:
Solves quadratic equations of the form ax² + bx + c = 0. Here, 'x' represents the roots, 'a', 'b', and 'c' are coefficients, and the term under the square root (b² - 4ac) is the discriminant.
Rigorous Derivation Tree
Divide through by leading coefficient 'a' and move constant term to the right-hand side.
Complete the square by adding (b / 2a)² to both sides of the equation.
Take the square root of both sides to isolate the linear binomial.
Subtract b / (2a) from both sides with correct ± sign.
CSCA Exam Triggers & Traps
Use when factoring by inspection is non-trivial, or when finding roots and discriminant Δ = b² - 4ac conditions.
Ensure equation is strictly in standard form ax² + bx + c = 0 before extracting coefficients a, b, c.
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