What you’ll learn
Solve quadratics using zero-product property.
Key idea
A zero product permits either factor to vanish; it does not require both factors to vanish at the same input.
A zero product splits into alternatives, not simultaneous vanishing; undo each signed factor constant and keep both roots.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve (x+6)(x-3)=0. Enter both roots separated by a comma.
- Zero product gives x+6=0 or x-3=0.
- Solve each signed linear factor: x=-6 or x=3; complete set -6, 3. Second missing factor constant is -3.
Answer: -6, 3
Quick Check
Evaluate a worked attempt at solve quadratics using zero-product property, identify the first invalid step, and provide the correction.
Solve (x+3)(x-7)=0: Step 1 sets either factor to zero. Step 2 concludes roots -3 and -7, copying the second signed factor constant. Locate the first invalid step and correct both roots.