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If f(x) = x^2 - 9, what are the roots of the polynomial?

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Question: If f(x) = x^2 - 9, what are the roots of the polynomial?

Options:

  1. -3 and 3
  2. 0 and 9
  3. 3 and 9
  4. 1 and -1

Correct Answer: -3 and 3

Solution: 

We can factor the polynomial as f(x) = (x - 3)(x + 3). Setting each factor to zero gives us the roots x = -3 and x = 3.

If f(x) = x^2 - 9, what are the roots of the polynomial?

Practice Questions

Q1
If f(x) = x^2 - 9, what are the roots of the polynomial?
  1. -3 and 3
  2. 0 and 9
  3. 3 and 9
  4. 1 and -1

Questions & Step-by-Step Solutions

If f(x) = x^2 - 9, what are the roots of the polynomial?
  • Step 1: Start with the function f(x) = x^2 - 9.
  • Step 2: Recognize that x^2 - 9 is a difference of squares, which can be factored.
  • Step 3: Factor the polynomial as f(x) = (x - 3)(x + 3).
  • Step 4: Set each factor equal to zero: x - 3 = 0 and x + 3 = 0.
  • Step 5: Solve the first equation: x - 3 = 0 gives x = 3.
  • Step 6: Solve the second equation: x + 3 = 0 gives x = -3.
  • Step 7: The roots of the polynomial are x = 3 and x = -3.
  • 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 roots of the polynomial.
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