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If f(x) = x^2 - 4, what are the roots of the polynomial?

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Question: If f(x) = x^2 - 4, what are the roots of the polynomial?

Options:

  1. -2 and 2
  2. 0 and 4
  3. 1 and -1
  4. 2 and 4

Correct Answer: -2 and 2

Solution: 

The polynomial can be factored as (x - 2)(x + 2). Setting each factor to zero gives us x - 2 = 0 or x + 2 = 0, so the roots are x = -2 and x = 2.

If f(x) = x^2 - 4, what are the roots of the polynomial?

Practice Questions

Q1
If f(x) = x^2 - 4, what are the roots of the polynomial?
  1. -2 and 2
  2. 0 and 4
  3. 1 and -1
  4. 2 and 4

Questions & Step-by-Step Solutions

If f(x) = x^2 - 4, what are the roots of the polynomial?
  • Step 1: Start with the polynomial f(x) = x^2 - 4.
  • Step 2: Recognize that this is a difference of squares, which can be factored.
  • Step 3: Factor the polynomial as (x - 2)(x + 2).
  • Step 4: Set each factor equal to zero: x - 2 = 0 and x + 2 = 0.
  • Step 5: Solve the first equation: x - 2 = 0 gives x = 2.
  • Step 6: Solve the second equation: x + 2 = 0 gives x = -2.
  • Step 7: The roots of the polynomial are x = 2 and x = -2.
  • Factoring Quadratic Polynomials – Understanding how to factor a quadratic expression to find its roots.
  • Setting Factors to Zero – Applying the zero product property to determine the values of x that make the polynomial equal to zero.
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