What a root is
A root is a value that balances both sides of an equation.
x² − 4x = 0. Try x = 4. Step 1 of 4
- Equation:
x² − 4x = 0. Tryx = 4. 16 − 16 = 0. It balances. 4 is a root.- Now try
x = 2. 4 − 8 = −4. Not zero. 2 is not a root.
The rule
First make the right side 0. Then put the value in place of x. Work out the left side. Compare it with 0. That is the whole test.
A root is a value that makes the equation true. It is also a zero of the polynomial ax² + bx + c.
Close does not count. The value must give exactly 0.
| Value | Working | Result | A root? |
|---|---|---|---|
| 0 | 0 − 0 | 0 | yes |
| 4 | 16 − 16 | 0 | yes |
| 2 | 4 − 8 | −4 | no |
| −2 | 4 + 8 | 12 | no |
This equation has two roots, 0 and 4. Some quadratics have one root. Some have none.
Now try it. Tap each value. See if both sides balance.
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