Mathematics: Analyzing the Quadratic Expression x^2 – 11x + 18 for Factors and Roots

x^2 – 11x + 18

To analyze the quadratic expression x^2 – 11x + 18, we can look at its factors and roots

To analyze the quadratic expression x^2 – 11x + 18, we can look at its factors and roots.

First, let’s try factoring the expression. We need to find two numbers that multiply to give 18 and add up to -11.

The possible pairs of factors of 18 are:
1, 18
2, 9
3, 6

Among these pairs, the pair that adds up to -11 is 2 and 9. Thus, we can factor the expression as:

(x – 2)(x – 9)

Now, if we set each factor equal to zero, we can find the roots of the quadratic equation:

(x – 2) = 0 or (x – 9) = 0

Solving these equations, we find that x = 2 and x = 9.

Therefore, the factors of the given expression are (x – 2) and (x – 9) and the roots are x = 2 and x = 9.

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