The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2.
How to determine a missing coefficient in a second order polynomial
Second order polynomials are represented graphically by parabolae and it may have two, one or no x-intercepts. The quantity of x-intercepts can be deducted from the discriminant of the quadratic formula, which is defined below:
For a · x² + b · x + c = 0, the discriminant is defined by:
d = b² - 4 · a · c (1)
There are three rules to determine the number of possible intercepts:
- If d < 0, then there are no x-intercepts.
- If d = 0, then there is only one x-intercept.
- If d > 0, then there are two x-intercepts.
Then, we have to find a value of b so that (1) has the following form:
b² - 4 · 3 · (-24) = 0
b² - 288 = 0
b = 12√ 2
The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2. [tex]\blacksquare[/tex]
Remark
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:
The graph of g(x) = 3 · x² + b · x - 24 has only one x-intercept. What is the value of b?
To learn more on parabolae, we kindly invite to check this verified question: https://brainly.com/question/10572747
