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Which polynomial has a root at x = 2?
Which polynomial has a root at x = 2?
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Practice Questions
1 question
Q1
Which polynomial has a root at x = 2?
x^2 - 4
x^2 + 4
x - 2
x + 2
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x^2 - 4 = 0 has roots at x = 2 and x = -2.
Questions & Step-by-step Solutions
1 item
Q
Q: Which polynomial has a root at x = 2?
Solution:
x^2 - 4 = 0 has roots at x = 2 and x = -2.
Steps: 6
Show Steps
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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