For ax² + bx + c = 0, the solutions are x = (−b ± √(b² − 4ac)) / (2a). Use it when factoring stalls. Quadratics as a topic are in quadratic equations.
Plug in carefully
Write a, b, and c with their signs. For x² − 5x + 6 = 0, a = 1, b = −5, c = 6. Then x = (5 ± √(25 − 24)) / 2, so x = 3 or x = 2. The quantity under the radical, b² − 4ac, tells you how many real solutions you get: positive is two, zero is one, negative is none on the ACT.
Completing the square is the same algebra without the frozen formula. That is in completing the square. Difference of squares is a faster factor when there is no middle term, in difference of squares.
The bottom line
List a, b, and c, keep the signs, then compute the formula once. Check both the + and the −. The formula list is in ACT Math formulas.
Start practicing
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