Quadratic Equations
Equal roots and triangle sides
Grade 11
Question:
<p><strong>Paragraph (Questions 11-13):</strong> \(a, b, c\) are the lengths of sides \(BC, CA, AB\) respectively of \(\triangle ABC\) satisfying \[\log\left(1 + \frac{c}{a}\right) + \log a - \log b = \log 2\] Also, the quadratic equation \(a(1-x^2) + 2bx + c(1+x^2) = 0\) has two equal roots.</p>
Step-by-Step Solution
Key Concept: Use the logarithmic constraint and the condition of equal roots in the quadratic to establish relationships between triangle sides.
<p>This is an introductory paragraph for questions 11-13. The actual questions are not shown in the provided text.</p>
Correct Answer: Unknown