College Algebra / Alg 211 · Procedure · 60–90 seconds
Solving with the Quadratic Formula
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Solving with the quadratic formula means reading a, b, and c from standard form, evaluating the discriminant, and finishing the formula with both signs.
Solve 2x² + 5x − 3 = 0. Read the coefficients: a = 2, b = 5, c = −3. The discriminant: b² − 4ac = 25 + 24 = 49 — positive, so two real solutions are coming, and √49 = 7 keeps them rational. The formula: x = (−5 ± 7)/4. The plus branch gives 2/4 = 1/2; the minus branch gives −12/4 = −3. Check both in the original: 2(1/4) + 5/2 − 3 = 0 and 2(9) − 15 − 3 = 0. The formula never fails on a quadratic; the only errors available are reading the coefficients wrong or dropping the ±.
The sign of c rides into the discriminant; −4ac with a negative c adds.
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