IPMAT Indore 2025Algebra > Medium(p+1p)(p + \frac{1}{p})(p+p1)2(p+1p)2(p + \frac{1}{p})2(p+p1)2(p+1p)22(\sqrt{p} + \frac{1}{\sqrt{p}})^22(p+p1)2(p+1p)2(\sqrt{p} + \frac{1}{\sqrt{p}})^2(p+p1)2✅ Correct Option: 3Related questions:Let f(x)=a2x2+2bx+cf(x) = a^2x^2 + 2bx + cf(x)=a2x2+2bx+c where, a≠0a \neq 0a=0, b,cb, cb,c are real numbers and xxx is a real variable thenIf 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 the harmonic mean of the roots of the equation (5+2)x2−bx+8+25=0(5 + \sqrt{2}) x ^ 2 - bx + 8 + 2\sqrt{5} = 0(5+2)x2−bx+8+25=0 is 444 then the value of bbb is