Final answer:
To find the value of a where g(a) = -4 for the function g(x) = 2x - 6/x, solve the quadratic equation 2a^2 + 4a - 6 = 0 using the quadratic formula.
Step-by-step explanation:
To find all a such that g(a) = -4 for the function g(x) = 2x - 6/x, we need to solve the equation 2a - 6/a = -4. We start by rearranging the equation:
- Multiply both sides by a to get rid of the denominator:
2a^2 - 6 = -4a - Add 4a to both sides to bring all terms to one side:
2a^2 + 4a - 6 = 0 - This is a quadratic equation, which can be solved using the quadratic formula a:
a = [-b ± √(b^2 - 4ac)]/(2a) - In our equation, a is 2, b is 4, and c is -6.
- Plug these values into the quadratic formula and solve for the two possible values of a.
After solving, you'll find that the values of a that satisfy the equation are the solutions to the quadratic equation.