Question

Form a quadratic polynomial one of whose zero is $2+\sqrt{5}$ and sum of zeroes is 4.

Answer 1

One root $\alpha =2+\sqrt{5}$ and another say $\beta$

Sum of roots$=\alpha +\beta =4$

$\Rightarrow 2+\sqrt{5}+\beta =4$

$\Rightarrow \beta =2-\sqrt{5}$

Polynomials, $p\left(x\right)=(x-2-\sqrt{5})(x-2+\sqrt{5})$

$p\left(x\right)=x^2-4x-1$