Question

show that the polynomial x to the power 4 + 4 x square + 6 has no zero

Answer 1

Given, f(x) = x4 + 4x2 + 6
               = (x2)2 + 4x2 + 6
Put x2 = a
Hence x4 + 4x2 + 6 = (x2)2 + 4x2 + 6
                             = a2 + 4a + 6
To find the zero of the above polynomial, we take a2 + 4a + 6 = 0
The above equation does not have a real root
Hence there is no zero for this given polynomial.