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natka813 [3]
3 years ago
11

Los puntos de intersección de los gráficos de f(x)=x2+6x−7 y g(x)=4x−10

Mathematics
1 answer:
alisha [4.7K]3 years ago
7 0

Answer:

Those graphs do not intersect.

Estes gráficos no se intersecciónan

Step-by-step explanation:

The intersection points are x for which:

f(x) = g(x)

In this question:

f(x) = x^{2} + 6x - 7

g(x) = 4x - 10

So

x^{2} + 6x - 7 = 4x - 10

x^{2} + 2x + 3 = 0

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

x^{2} + 2x + 3 = 0

So a = 1, b = 2, c = 3

\bigtriangleup = b^{2} - 4ac = 2^{2} - 4*1*3 = -8

Sincce \bigtriangleup is negative, there are no solutions, which means that those graphs do not intersect.

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