Respuesta :
Answer:
The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.
Step-by-step explanation:
Suppose we have a function y = f(x). The zeros, which are the values of x for which y = 0, are also called the x-intercepts of the function.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
I will write the function as a function of x, just exchanging a for x.
[tex]f(x) = x^{2} + 5x + 6[/tex]
[tex]\bigtriangleup = 5^{2} - 4*1*6 = 1[/tex]
[tex]x_{1} = \frac{-5 + \sqrt{1}}{2*1} = -2[/tex]
[tex]x_{2} = \frac{-5 - \sqrt{1}}{2*1} = -3[/tex]
The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.
