Answer:
B
Step-by-step explanation:
Using the determinant to determine the type of zeros
Given
f(x) = ax² + bx + c ( a ≠ 0 ) ← in standard form, then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct zeros
• If b² - 4ac = 0 then 2 real and equal zeros
• If b² - 4ac < 0 then 2 complex zeros
Given
f(x) = (x - 1)² + 1 ← expand factor and simplify
= x² - 2x + 1 + 1
= x² - 2x + 2 ← in standard form
with a = 1, b = - 2, c = 2, then
b² - 4ac = (- 2)² - (4 × 1 × 2) = 4 - 8 = - 4
Since b² - 4ac < 0 then the zeros are complex
Thus P(x) has no real zeros
The ratio of the distance between the foci and the length of the <em>major</em> axis is called eccentricity.
<h3>
Definitions of dimensions in ellipses</h3>
Dimensionally speaking, an ellipse is characterized by three variables:
- Length of the <em>major</em> semiaxis (
). - Length of the <em>minor</em> semiaxis (
). - Distance between the foci and the center of the ellipse (
).
And there is the following relationship:
(1)
Another variable that measure how "similar" is an ellipse to a circle is the eccentricity (
), which is defined by the following formula:
,
(2)
The greater the eccentricity, the more similar the ellipse to a circle.
Therefore, the ratio of the distance between the foci and the length of the <em>major</em> axis is called eccentricity. 
To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943
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Answer:
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