Quadratic Formula
Solves any equation of the form ax² + bx + c = 0 for x
The equation
What it solves
Solves any equation of the form ax² + bx + c = 0 for x. In kinematics it appears whenever you set two position expressions equal and time is the unknown.
When to use it
Whenever a kinematic equation produces a quadratic in t (or any other unknown). Both roots are algebraically valid; physics context usually selects the positive, future root.
When NOT to use it
Not needed if the equation factors cleanly or if one root is obviously unphysical (negative time). For near-zero discriminants, check whether the quadratic reduces to a repeated root representing a special physical case.
Common mistakes
Sign errors: b² − 4ac must use the coefficient b, not the whole term bx. Forgetting the ± and discarding the second root before checking its physical meaning. Dividing only the numerator or only the square-root term by 2a instead of the whole expression.