1. The problem asks what knowledge scientists gained by studying Rosalind Franklin's 1952 X-ray photograph of DNA. 2. This photograph is famous for revealing the structural pattern of DNA through X-ray diffraction. 3. The key feature in the image is the "X" shape formed by dark bands and spots, which is characteristic of a helical structure. 4. Scientists interpreted this pattern as evidence of the double-helix structure of DNA. 5. The other options (sequence of DNA, mutation, role in protein synthesis) are not directly revealed by this photograph. 6. Therefore, the correct answer is that the photograph gave knowledge about the double-helix structure of DNA. Final answer: double-helix structure of DNA