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If a polynomial f(x) = x^2 - 5x + 6, what are its roots?

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Question: If a polynomial f(x) = x^2 - 5x + 6, what are its roots?

Options:

  1. 1 and 6
  2. 2 and 3
  3. 3 and 2
  4. 5 and 1

Correct Answer: 2 and 3

Solution: 

Factoring gives (x-2)(x-3) = 0, so roots are 2 and 3.

If a polynomial f(x) = x^2 - 5x + 6, what are its roots?

Practice Questions

Q1
If a polynomial f(x) = x^2 - 5x + 6, what are its roots?
  1. 1 and 6
  2. 2 and 3
  3. 3 and 2
  4. 5 and 1

Questions & Step-by-Step Solutions

If a polynomial f(x) = x^2 - 5x + 6, what are its roots?
Correct Answer: 2 and 3
  • Step 1: Start with the polynomial f(x) = x^2 - 5x + 6.
  • Step 2: We need to find two numbers that multiply to the constant term (6) and add up to the coefficient of x (-5).
  • Step 3: The two numbers that work are -2 and -3 because (-2) * (-3) = 6 and (-2) + (-3) = -5.
  • Step 4: Rewrite the polynomial using these numbers: f(x) = (x - 2)(x - 3).
  • Step 5: Set the factored form equal to zero: (x - 2)(x - 3) = 0.
  • Step 6: Solve for x by setting each factor to zero: x - 2 = 0 or x - 3 = 0.
  • Step 7: This gives us the solutions: x = 2 and x = 3.
  • Step 8: Therefore, the roots of the polynomial are 2 and 3.
  • Factoring Polynomials – The process of expressing a polynomial as a product of its factors to find its roots.
  • Finding Roots – Identifying the values of x for which the polynomial equals zero.
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