Due to length restrictions, we cannot summarize the results of the three parts about the <em>quadratic</em> equations of the form x² + b · x + c = 0. We kindly invite to check the explanation for further details.
<h3>How to apply algebra properties to solve quadratic equations of the form x² + b · x + c = 0</h3>
In this question we have several exercises with <em>quadratic</em> equations of the form x² + b · x + c = 0 and, to be more exactly, <em>quadratic</em> equations with the following characteristics:
x² - (r₁ + r₂) · x + r₁ · r₂ = 0 (1)
Please notice that the <em>first grade</em> coefficient is equal to the inverse of the sum of the two roots and the <em>zero grade</em> coefficient is the product of the two coefficients.
Now we proceed to resolve all the points:
Part I
a) (x + 17) · (x + 1) = x² + 18 · x + 18, r₁ = - 17, r₂ = - 1
b) (x + 5) · (x + 4) = x² + 9 · x + 20, r₁ = - 5, r₂ = - 4
c) (x - 11) · (x - 1) = x² - 12 · x + 11, r₁ = 11, r₂ = 1
d) (x - 18) · (x - 2) = x² - 20 · x + 36, r₁ = 18, r₂ = 2
Part II
a) x² - 12 · x + 27
b) (x + 4) · (x + 8)
c) (x - 5) · (x - 7)
d) (x - 4) · (x - 5)
Part III
a) (x - 18) · (x + 3) = x² - 15 · x - 54
b) (x + 18) · (x + 3) = x² + 21 · x + 54
c) (x + 18) · (x - 3) = x² + 15 · x - 54
d) (x - 18) · (x - 3) = x² - 21 · x + 54
To learn more on quadratic equations: brainly.com/question/17177510
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