Number of distinct quadratic equations with real roots such that the equation remains unchanged if their roots are cubed is equal to
Step-by-Step Solution
Key Concept: If $\alpha,\beta$ are roots and $\alpha^3,\beta^3$ are also roots (same equation), then $\{\alpha^3,\beta^3\}=\{\alpha,\beta\}$. Cases: $\alpha^3=\alpha$ or $\alpha^3=\beta$ and $\beta^3=\alpha$.
6 distinct quadratic equations.
Correct Answer: 6