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If x^2 - 6x + 9 = 0, what is the repeated root?

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Question: If x^2 - 6x + 9 = 0, what is the repeated root?

Options:

  1. 3
  2. 6
  3. 9
  4. 0

Correct Answer: 3

Solution: 

The polynomial can be factored as (x - 3)(x - 3) = 0, giving a repeated root of x = 3.

If x^2 - 6x + 9 = 0, what is the repeated root?

Practice Questions

Q1
If x^2 - 6x + 9 = 0, what is the repeated root?
  1. 3
  2. 6
  3. 9
  4. 0

Questions & Step-by-Step Solutions

If x^2 - 6x + 9 = 0, what is the repeated root?
  • Step 1: Start with the equation x^2 - 6x + 9 = 0.
  • Step 2: Recognize that this is a quadratic equation in the form of ax^2 + bx + c.
  • Step 3: Identify the coefficients: a = 1, b = -6, c = 9.
  • Step 4: Look for two numbers that multiply to c (9) and add to b (-6).
  • Step 5: The numbers -3 and -3 work because -3 * -3 = 9 and -3 + -3 = -6.
  • Step 6: Rewrite the quadratic equation using these numbers: (x - 3)(x - 3) = 0.
  • Step 7: Set each factor equal to zero: x - 3 = 0.
  • Step 8: Solve for x: x = 3.
  • Step 9: Since both factors are the same, x = 3 is a repeated root.
  • Quadratic Equations – Understanding how to solve quadratic equations using factoring and identifying repeated roots.
  • Factoring – The ability to factor a perfect square trinomial.
  • Roots of Polynomials – Identifying the roots of a polynomial equation and recognizing when they are repeated.
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