Question

If \(\alpha, \beta, \gamma, \delta, \epsilon\) are the roots of the equation \(x^5 + x^4 - 13x^3 - 13x^2 + 36x + 36 = 0\) and \(\alpha<\beta<\gamma<\delta<\epsilon\) then \( \frac{\epsilon}{\alpha} + \frac{\delta}{\beta} + \frac{1}{\gamma} = \)

• A. 0
• B. 1
• C. -1
• D. -3

Hint:

When factoring high-degree polynomials, always look for simple patterns like factoring by grouping. If the powers of the variable decrease in a regular way (e.g., x^4, x^2, constant), you can often make a substitution (like y=x^2) to reduce it to a simpler polynomial.

Answer 1

The Correct Option is D