Final Answer:
The absolute value of the two symmetric real roots for the polynomial g(x) = 2x^4 + 0.5x^2 - 3 is approximately 1.118.
Step-by-step explanation:
Given polynomial: g(x) = 2x^4 + 0.5x^2 - 3
Set g(x) equal to zero to find the roots: 2x^4 + 0.5x^2 - 3 = 0
Let y = x^2, then the equation becomes quadratic: 2y^2 + 0.5y - 3 = 0
Solve for y using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a)
Substitute y back as x^2 and solve for x to get the roots.
The roots are symmetric, so we only need to consider one side.
Calculate the absolute value of one root, and since they are symmetric, the absolute value of the other root is the same.
The absolute value is approximately 1.118.