PEAZIT Aha card
Go straight to resources ↓Quadratic inequalities: test the intervals
The roots split the number line into intervals. Check each factor’s sign in each interval. Opposite signs give a negative product.
| Expression | Meaning |
|---|---|
| x < 1: (−) · (−) = + | Left of both roots, both factors are negative. |
| 1 < x < 4: (+) · (−) = − | Between the roots, the factors have opposite signs. |
| x > 4: (+) · (+) = + | Right of both roots, both factors are positive. |
One worked example
- x < 1: (−) · (−) = +Left of both roots, both factors are negative.
- 1 < x < 4: (+) · (−) = −Between the roots, the factors have opposite signs.
- x > 4: (+) · (+) = +Right of both roots, both factors are positive.
Watch out: A negative leading coefficient reverses the interval signs. A repeated root need not change the sign.
Goal, prerequisites and card origin
What you will learn: Find where a factored quadratic expression is negative.
What you need first: Quadratic roots and signs of a product.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
The roots split the number line into intervals. Check each factor’s sign in each interval. Opposite signs give a negative product.