IPMAT Indore 2024Algebra > Medium10\sqrt{10}10252\sqrt{5}257\sqrt{7}7272\sqrt{7}27✅ Correct Option: 4Related questions:If a1,a2,...,a8a_1, a_2, ..., a_8a1,a2,...,a8 are the roots of the equation x8+x7+...+x+1=0x^8 + x^7 + ... + x + 1 = 0x8+x7+...+x+1=0, then the value of a12025+a22025+...+a82025a_1^{2025} + a_2^{2025} + ... + a_8^{2025}a12025+a22025+...+a82025 isIf 8x2−2kx+k=08x^2 - 2kx + k = 08x2−2kx+k=0 is a quadratic equation in xxx, such that one of its roots is ppp times the other, and p,kp, kp,k are positive real numbers, then kkk equalsThe number of real solutions of the equation (x2−15x+55)x2−5x+6=1(x^2 - 15x + 55)^{x^2-5x+6} = 1(x2−15x+55)x2−5x+6=1 is: