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julsineya [31]
2 years ago
10

PLEASE HELP

Mathematics
1 answer:
Simora [160]2 years ago
7 0

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:

  1. If <em>d < 0</em>, then there are no <em>x</em>-intercepts.
  2. If <em>d = 0</em>, then there is only one <em>x</em>-intercept.
  3. 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. \blacksquare

<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

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