ACT Preparation / Unit 11 ACT 1006 worked example, 60 to 90 seconds
Choosing a Method for a Quadratic
The idea
A quadratic equation is solved fastest by the method its form invites. Step one: if a squared expression stands alone, or there is no x term, use the square root property. Step two: otherwise, set the equation equal to zero and try to factor; if two numbers with the right product and sum appear quickly, use the zero-product property. Step three: if factoring stalls, use the quadratic formula, which never fails.
In practice
Worked example: three equations. 4x² = 49 has no x term: x² = 49/4, so x = ±7/2. x² + 2x − 15 = 0 factors as (x + 5)(x − 3), so x = −5 or 3. x² + 2x − 4 = 0 does not factor over the integers, so use the formula: x = (−2 ± √20)/2 = −1 ± √5.
Where people slip
Every method gives the same solutions; the choice only saves time. When in doubt, the formula is always available.
Your place on the trail
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