Question

The roots of the characteristic equation \(2S^3 + 3S^2 + 4S + 6 = 0\) are

• A. \(S = -1.5, S = \pm \sqrt{2}\)
• B. \(S = -1, S = \pm \sqrt{2}\)
• C. \(S = -1, S = -4, S = -6\)
• D. \(S = -1, S = -2, S = -3\)

Hint:

When solving cubic equations, use factorization and root-finding techniques such as synthetic division or numerical methods.

Answer 1

The Correct Option is A

The given characteristic equation \(2S^3 + 3S^2 + 4S + 6 = 0\) is a cubic equation. By using the appropriate methods, such as factoring or applying the cubic formula, the roots are found to be \(S = -1.5, S = \pm \sqrt{2}\), indicating a combination of real and complex roots.