What is the relation between \alpha and \beta?
For the following two (02) items: Let \alpha and \beta be the roots of the quadratic equation x^2+(\log_{0.5}(a^2))x+(\log_{0.5}(a^2))^4=0 where a^2 \neq 1 and \log_{0.5}(a^2) \gt 0. Further, \beta^2=\alpha(\log_{a^2}(0.5)).
- A. \alpha=2\beta
- B. 2\alpha=\beta
- C. \alpha=-2\beta
- D. 2\alpha=-\beta ✓
Correct Answer: D. 2\alpha=-\beta
Explanation
Using the relation derived earlier, \alpha = B\beta^2. The specific structural properties of the equation parameters imply the relationship 2\alpha = -\beta under valid domain constraints for a.
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