Which of the following is true for the polynomial x^2 - 5x + 6?
Correct Answer: The polynomial has two real roots.
- Step 1: Identify the polynomial given, which is x^2 - 5x + 6.
- Step 2: To find the roots, we need to factor the polynomial.
- Step 3: Look for two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of x).
- Step 4: The numbers -2 and -3 work because -2 * -3 = 6 and -2 + -3 = -5.
- Step 5: Write the factored form of the polynomial: (x - 2)(x - 3).
- Step 6: Set each factor equal to zero to find the roots: x - 2 = 0 and x - 3 = 0.
- Step 7: Solve for x in each equation: x = 2 and x = 3.
- Step 8: Conclude that the polynomial has two real roots: x = 2 and x = 3.
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