How to solve
A monic quadratic x² + bx + c factors when you find two numbers that multiply to c and add to b. Those numbers are the roots with opposite sign in (x − r₁)(x − r₂) = 0, because a product is zero exactly when a factor is zero.
Steps
- Find two numbers that multiply to c and add to b in x² + bx + c.
- Write the factorization (x − r₁)(x − r₂) = 0.
- Read the roots r₁ and r₂ (order them as required by the drill).
Example
Find the roots of x² − x − 6 = 0.
- Need two numbers that multiply to −6 and add to −1: −3 and 2.
- Factor: (x − 2)(x + 3) = 0.
- Roots: x = 2 or x = −3; listed ascending: −3, 2.
Answer: -3, 2
How to type answers
- Enter roots as a, b with a ≤ b, e.g. -3, 2
Loading drills…