Question

If one zero of the polynomial ${\displaystyle x^2-4x+1is(2+\sqrt{3})}$ , write the other zero. 

Answer 1

Let the other zeroes of ${\displaystyle x^2–4x+1}$ be a.
By using the relationship between the zeroes of the quadratic polynomial. 

We have, sum of zeroes =${\displaystyle \frac{-\left(\text{Coefficient of x}\right)}{\left(\text{Coefficient of}{x}^2\right)}}$ 

∴${\displaystyle 2+\sqrt{3}+a=-\frac{(-4)}{1}}$ 

⇒${\displaystyle a=2–\sqrt{3}}$ 

Hence, the other zeroes of${\displaystyle x^2–4x+1is2–\sqrt{3}}$