Respuesta :
Answer:
Those graphs do not intersect.
Estes gráficos no se intersecciónan
Step-by-step explanation:
The intersection points are x for which:
[tex]f(x) = g(x)[/tex]
In this question:
[tex]f(x) = x^{2} + 6x - 7[/tex]
[tex]g(x) = 4x - 10[/tex]
So
[tex]x^{2} + 6x - 7 = 4x - 10[/tex]
[tex]x^{2} + 2x + 3 = 0[/tex]
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:
[tex]x^{2} + 2x + 3 = 0[/tex]
So [tex]a = 1, b = 2, c = 3[/tex]
[tex]\bigtriangleup = b^{2} - 4ac = 2^{2} - 4*1*3 = -8[/tex]
Sincce [tex]\bigtriangleup[/tex] is negative, there are no solutions, which means that those graphs do not intersect.
