Question: If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots?
Options:
2 and 3
1 and 6
3 and 2
0 and 6
Correct Answer: 2 and 3
Solution:
Factoring the polynomial P(x) gives (x - 2)(x - 3), so the roots are 2 and 3.
If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots?
Practice Questions
Q1
If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots?
2 and 3
1 and 6
3 and 2
0 and 6
Questions & Step-by-Step Solutions
If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots?
Step 1: Start with the polynomial P(x) = x^2 - 5x + 6.
Step 2: Look for 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: P(x) = (x - 2)(x - 3).
Step 5: To find the roots, set each factor equal to zero: x - 2 = 0 and x - 3 = 0.
Step 6: Solve for x in each equation: x = 2 and x = 3.
Step 7: The roots of the polynomial are 2 and 3.
Factoring Polynomials – The process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.
Finding Roots – Identifying the values of x for which the polynomial equals zero, which correspond to the x-intercepts of the graph of the polynomial.
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