Question

prove that 4x⁴+12x²+15 has no zero

Answer 1

$4 {x}^{4} + 12 {x}^{2} + 15 = 0 \\ 4 {x}^{4} + 12 {x}^{2} + 9 + 6 = 0 \\ {(2 {x}^{2} + 3) }^{2} = - 6 \\ \\ 2 {x}^{2} + 3 = \sqrt{ - 6 } \\ \sqrt{ - 6 } \: is \: an \: imaginary \: number \: hence\\ \: it \: doesnot \: have \: real \: roots$