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Answer :
Final answer:
To factor x² + 12x² - 15x + 45 using Euler's approach, we need to find the values of p and q. The formula n = 4x + 50 can be used to find the value of n. By comparing the coefficients, we can determine that p = q.
Explanation:
In order to factor x² + 12x² - 15x + 45 using Euler's approach, we need to find the values of p and q. We can expand the given quadratic expression as (x² + px + α)(x² + qx + β) and compare the coefficients to determine that p = q.
First, let's find x by using the plus-four method. We have x = 15. Next, let's find n using the formula n = 4x + 50. Plugging in the value of x, we get n = 54.
Now, we can calculate the values of p and q. We have p = 15/54 ≈ 0.278 and q = 1 - p ≈ 0.722. Therefore, p is not equal to q in this case.
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