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For what values of a does the equation 3ax² + 5xy + (a² − 2)y² = 0 represent a pair of straight lines that are mutually perpendicular?

1. for two distinct values of a
2. for every value of a
3. for exactly one value of a
4. for no value of a

Correct answer: for two distinct values of a

Solution

The equation represents a pair of straight lines that are mutually perpendicular when the discriminant condition is satisfied, which leads to two distinct values of 'a' that fulfill this requirement.

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