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Let p, q, r be non-zero real numbers. The equations 2a²x² - 2abx + b² = 0 and p²x² + 3pqx + q² = 0 are such that they:

1. have no common root
2. have exactly one common root if 2a² + b² = p² + q²
3. have two common roots if 3pq = 2ab
4. have two common roots if 3qb = 2ap

Correct answer: have no common root

Solution

The two quadratic equations can be analyzed for common roots by examining their discriminants and coefficients. If the conditions for having common roots are not satisfied, as indicated in the problem, then the equations will not share any roots, confirming that option A is correct.

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