<em>k</em> must be greater than or equal to 22.75 to have two <em>different</em> zeros.
<h3>How to determine the value of missing coefficient in second order polynomials</h3>
<em>Second order</em> polynomials are <em>algebraic</em> expressions that observe the following form:
(1)
Where:
- a, b, c - Coefficients
- x - Independent variable
For polynomials of the form <em>p(x) = 0</em>, we can infer the nature of their roots by applying the following discriminant:
<em>d = b² - 4 · a · c</em> (2)
According to (2), there are three cases:
- If <em>d < 0</em>, then there are two <em>conjugated complex</em> roots.
- If <em>d = 0</em>, then the two roots are the <em>same real</em> number.
- If <em>d > 0</em>, then the two roots are two <em>distinct real</em> numbers.
Now we have the following <em>discriminant</em> case:
<em>-(3 + 2 · k)² - 4 · (1) · (4) ≠ 0</em>
<em>-(9 + 6 · k + 4 · k²) - 16 ≠ 0</em>
<em>-9 - 6 · k - 4 · k² - 16 ≠ 0</em>
<em>4 · k²+ 6 · k +25 ≠ 0</em>
<em />
This characteristic polynomial has two conjugated complex roots, then we conclude that all values of <em>k</em> must positive or negative, but never zero. By graphng tools we find that <em>k</em> must be greater than or equal to 22.75 to have two <em>different</em> zeros.
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