Final answer:
To solve the quadratic equation f(x)=2x²-6x-2, we apply the quadratic formula using the coefficients a=2, b=-6, and c=-2, computing the determinant and square root, and then solving for x, rounding to the nearest hundredth.
Step-by-step explanation:
The student's question involves solving a specified quadratic function, f(x)=2x²-6x-2. To find the roots of this equation, we can use the quadratic formula, which is expressed as:
x = (-b ± √(b²-4ac))/(2a) for a quadratic equation of the form ax²+bx+c=0.
In our case, the function can be rewritten to match this form by bringing it to zero: 2x²-6x-2=0. Our coefficients are a=2, b=-6, and c=-2. Plugging these into the quadratic formula, we perform the necessary computations to find the values of x that satisfy the equation. These steps include calculating the determinant (b²-4ac), taking its square root, and applying the formula to obtain two solutions for x. We round the solutions to the nearest hundredth if necessary, providing the final answer.