Question

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

Answer 1

Those graphs do not intersect.

Estes gráficos no se intersecciónan

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\\eq0`.

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) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\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.