Question

If one zero of the polynomial x² – 4x + 1 is `(2 + sqrt(3))`, write the other zero.

Answer 1

Let the other zeroes of x² – 4x + 1 be a.

By using the relationship between the zeroes of the quadratic polynomial. 

We have, sum of zeroes = `(-("Coefficient of"  x))/(("Coefficient of"  x^2))` 

∴ `2 + sqrt(3) + a = -((-4))/1` 

⇒ `a = 2 - sqrt(3)` 

Hence, the other zeroes of x² – 4x + 1 is `(2 - sqrt(3))`.