Answer:
Explanation:
To find the value of the negative zero of the function g(x), we need to find the zero of the function. The zero of a function is the value of x at which the function equals zero.
We can find the zero of the function g(x) by setting it equal to zero and solving for x:
3x^2 - 15x - 42 = 0
Dividing both sides by 3 to simplify:
x^2 - 5x - 14 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
Plugging in the values, we get:
x = (-(-5) ± sqrt((-5)^2 - 4(1)(-14))) / 2(1)
x = (5 ± sqrt(81)) / 2
x = (5 ± 9) / 2
So, the solutions for x are:
x = 7 or x = -2
Therefore, the negative zero of the function g(x) is -2.