Which polynomial has a root at x = 2?
Correct Answer: x^2 - 4 = 0
- Step 1: Understand what a root of a polynomial is. A root is a value of x that makes the polynomial equal to zero.
- Step 2: We want to find a polynomial that has a root at x = 2. This means we need to create an equation that equals zero when we substitute x with 2.
- Step 3: Start with the simplest polynomial form, which is (x - 2). This polynomial will equal zero when x = 2.
- Step 4: To create a polynomial, we can square (x - 2). This gives us (x - 2)(x - 2) = (x - 2)^2.
- Step 5: Expand (x - 2)^2 to get x^2 - 4x + 4. This is a polynomial that has a root at x = 2.
- Step 6: Alternatively, we can use the polynomial x^2 - 4, which can be factored as (x - 2)(x + 2). This also has a root at x = 2.
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