The value of <em>b</em> so that 3 · x² + b · x - 24 has the same <em>x</em>-intercepts (only one <em>x</em>-intercept) is 12 √2.
<h3>How to determine a missing coefficient in a second order polynomial</h3>
<em>Second order</em> polynomials are represented graphically by parabolae and it may have two, one or no <em>x</em>-intercepts. The quantity of <em>x</em>-intercepts can be deducted from the discriminant of the quadratic formula, which is defined below:
For <em>a · x² + b · x + c = 0</em>, the discriminant is defined by:
<em>d = b² - 4 · a · c</em> (1)
There are three rules to determine the number of possible intercepts:
- If <em>d < 0</em>, then there are no <em>x</em>-intercepts.
- If <em>d = 0</em>, then there is only one <em>x</em>-intercept.
- If <em>d > 0</em>, then there are two <em>x</em>-intercepts.
Then, we have to find a value of <em>b</em> so that (1) has the following form:
<em>b² - 4 · 3 · (-24) = 0</em>
<em>b² - 288 = 0</em>
<em>b = 12√ 2</em>
The value of <em>b</em> so that 3 · x² + b · x - 24 has the same <em>x</em>-intercepts (only one <em>x</em>-intercept) is 12 √2. 
<h3>Remark</h3>
The answer choices do not correspond with the given statement, the phrase "same x-intercepts" may lead to confusion and possible graph cannot be found. A possible corrected statement is shown below:
<em>The graph of g(x) = 3 · x² + b · x - 24 has only one x-intercept. What is the value of </em><em>b</em><em>?</em>
To learn more on parabolae, we kindly invite to check this verified question: brainly.com/question/10572747
