Question

If f(x)=x squared-2x and g(x) = 6x+4 for which is a value of x does (f+g)(x) =0

Answer 1

For
`x = -2`

Explanation:

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 + √(\Delta))/(2*a)`

`x_(2) = (-b - √(\Delta))/(2*a)`

`\Delta = b^(2) - 4ac`

In this question:

`f(x) = x^2 - 2x`

`g(x) = 6x + 4`

`f(x) + g(x) = (f+g)(x)  = x^2 - 2x + 6x + 4 = x^2 + 4x + 4`

Which is a value of x does (f+g)(x) =0

`x^2 + 4x + 4`

Quadratic equation with
`a = 1, b = 4, c = 4`

So

`\Delta = 4^(2) - 4*1*4 = 0`

`x_(1) = (-4 + √(0))/(2) = -2`

`x_(2) = (-4 - √(0))/(2) = -2`

For
`x = -2`