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If a polynomial f(x) = x^2 - 5x + 6, what are its roots?
If a polynomial f(x) = x^2 - 5x + 6, what are its roots?
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Practice Questions
1 question
Q1
If a polynomial f(x) = x^2 - 5x + 6, what are its roots?
1 and 6
2 and 3
3 and 2
5 and 1
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Factoring gives (x-2)(x-3) = 0, so roots are 2 and 3.
Questions & Step-by-step Solutions
1 item
Q
Q: If a polynomial f(x) = x^2 - 5x + 6, what are its roots?
Solution:
Factoring gives (x-2)(x-3) = 0, so roots are 2 and 3.
Steps: 8
Show Steps
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.
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