Question

If one zero of the polynomial `x^2 - 4x + 1` is `(2 + sqrt(3))`, write the other zero.

Answer 1

Let the other zero of the given polynomial be a.  

Now, Sum of the zeroes of the given polynomial = `-(-4)/1 = 4` 

∴ `a + (2 + sqrt(3)) = 4` 

⇒ `a = 4 - 2 - sqrt(3)` 

⇒ `a = 2 - sqrt(3)` 

Hence, the other zero of the given polynomial is `(2 - sqrt(3))`.