No, no, no, Dumbledore did seek and attempt to find about the Horcruxes, for a long time. All the lengths to which he went, such as talking to Bob Ogden, the Ministry Law Enforcement official before he died, talking with the co-founder of Borgin and Burkes, getting memory from Morphin Gaunt in Azkabhan, getting memory from Hokie the house-elf of Hemzibar Smith, etc., all showed that Dumbledore suspected and tried hard to find the whereabouts of the Horcruxes for a long time. He only needed Slughorn's memory to once-and-for-all confirm that Voldemort created Horcruxes and he wanted to know exactly how many did Voldemort create.

Dumbledore did seek and attempt to find about the Horcruxes, for a long time. All the lengths to which he went, such as talking to Bob Ogden, the Ministry Law Enforcement official before he died, talking with the co-founder of Borgin and Burkes, getting the memory from Morphin Gaunt in Azkaban, getting memory from Hokie the house-elf of Hepzibah Smith, etc., all showed that Dumbledore suspected and tried hard to find the whereabouts of the Horcruxes for a long time. He only needed Slughorn's memory to know once-and-for-all that Voldemort created Horcruxes and he wanted to know exactly how many did Voldemort create.