ACT Preparation / Unit 11 ACT 1007 worked example, 60 to 90 seconds
Solving With the Quadratic Formula
The idea
The quadratic formula is applied in four steps. First, write the equation in the form ax² + bx + c = 0 and read a, b and c with their signs. Second, compute the discriminant, b² − 4ac. Third, substitute into the formula. Fourth, simplify the radical and reduce the fraction, dividing every term of the numerator by any common factor.
In practice
Worked example: 3x² = 2x + 4. Step one: 3x² − 2x − 4 = 0, so a = 3, b = −2 and c = −4. Step two: (−2)² − 4(3)(−4) = 4 + 48 = 52. Step three: x = (2 ± √52)/6. Step four: √52 = 2√13, so x = (2 ± 2√13)/6 = (1 ± √13)/3.
Where people slip
When b is negative, −b is positive: with b = −2, the formula starts with +2. Reduce only if the factor divides every term in the numerator.
Your place on the trail
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