Respuesta :

arodri04

Answer:

x=0 and -2

Notice a n=8, g(n)=0 and f(x) = 0.  If n<8, the coefficients for f(x) become negative and when n>8, the coefficients becomes positive.  It won't affect x=0 because x can be factor out and be equal to zero but will affect the second zero

Step-by-step explanation:

Given:  g(n) = 1/2*n - 4 and f(x)= g(n)x^2 + 2(g(n))x; n≠8

n = 2

g(n) = 1/2*n - 4

g(n) = 1/2*2 - 4 = 1-4 = -3

f(x)= g(n)x^2 + 2(g(n))x

f(x)= -3x^2 + 2(-3)x = -3x^2 - 6x

0=  -3x^2 - 6x; factor out -3x

0 = -3x(x + 2)

-3x = 0; x=0

(x+2)= 0; x=-2

Notice a n=8, g(n)=0 and n<8, the coefficients for f(x) become negative and when n>8, the coefficients becomes positive

facundo3141592

The zeros of the quadratic function when n = 2 are:

x = 0 and x = -2.

How to find the zeros of f(x)?

We know that:

g(n) = (1/2)*n - 4

Then:

g(2) = (1/2)*2 - 4 = -3

So we can write:

f(x) = g(2)*x^2 + 2*g(2)*x

f(x) = -3*x^2 - 6x

We want to find the zeros of that, so we need to solve:

-3*x^2 - 6x = 0

If we take x as a common factor, we can write:

(-3x - 6)*x = 0

Then one zero is when x = 0, the other is when:

-3x - 6 = 0

-3x = 6

x = 6/-3 = -2

So the zeros are at x = 0 and x = -2

If you want to learn more about zeros.

https://brainly.com/question/11514041

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