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Consider the function f(x) = 3x2 + 7x + 2. What is the value of the discriminant? –17253173 How many x-intercepts does this function have? 0123 What are the number of zeros for this function? zero real number solutionsone real number solutiontwo real number solutions

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carlosego
What is the value of the discriminant?
 For this case, the discriminant will be given by
 b ^ 2 - 4 * a * c
 Where
 b = 7
 a = 3
 c = 2
 substituting
 b ^ 2 - 4 * a * c = (7) ^ 2 - 4 * (3) * (2) = 25
 Therefore the value of the discriminant is 25.
 How many x-intercepts does this function have?
 It has two intercepts with the x axis and can be found by equaling the function to zero. That is to say,
 3x2 + 7x + 2 = 0
 The results will be the interceptions with x.
 What are the number of zeros for this function?
 The number of zeros for this function is
 two real number solutions
 Because it is a quadratic function.

Using quadratic function concepts, it is found that:

  • The value of the discriminant is of 25.
  • Since it is positive, the function has two real number solutions.

Discriminant:

The discriminant of a quadratic function in the format [tex]y = ax^2 + bx + c[/tex] is given by:

[tex]\Delta = b^2 - 4ac[/tex]

The discriminant is related to the number of x-intercepts, as follows:

  • If [tex]\Delta > 0[/tex], the function has two x-intercepts.
  • If [tex]\Delta = 0[/tex], the function has one x-intercept.
  • If [tex]\Delta < 0[/tex], the function has no x-intercepts.

In this problem, the function is:

[tex]f(x) = 3x^2 + 7x + 2[/tex]

  • Hence the coefficients are [tex]a = 3, b = 7, c = 2[/tex].

Then:

[tex]\Delta = b^2 - 4ac = 7^2 - 4(3)(2) = 49 - 24 = 25[/tex]

  • The value of the discriminant is of 25.
  • Since it is positive, the function has two real number solutions.

To learn more about quadratic function concepts, you can take a look at https://brainly.com/question/19776811

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