Question

Which among the expressions 1 - 1/16z² and z² + z + 1 is a polynomial in z? Find its zeroes and degree.

Answer 1

The highest power is 2, so the degree is also 2, in both the expressions.

Equating the expression with 0,

1 - 1/16z² = 0

1 = 1/16z²

x² =16

∴ x = ±4

Yes, the above expression (1 - 1/16z²) is a polynomial, and its zeroes are 4 & -4.

Equating the expression with 0,

z² + z + 1 =0

Using Sreedharacharya formula, 

∵ it does not have real values.

∴ The zeroes of z² + z + 1 are complex numbers, though it is a polynomial having the degree 2.