Question

If one zero of the polynomial x²− 4x + 1 is 2 + √3​, find another zero.

Answer 1

To find another zero of the polynomial x²− 4x + 1 , if one of them will be (2 +√3​).

Let consider two zeros α, β

(x²− 4x + 1 comparing with general equation ax²+ bx + c, then a = 1,b =−4,c = 1)

α + β = 4

from equation (1) & (2)

α + β = 4

2 + √3 ​+ β = 4

β = 4−(2 + √3​)

β = 4 − 2 − √3​

β = 2 − √3​