Question

Write a polynomial that has the lowest degree, a leading coefficient of 2, and 1/2 and 3 + √5 as roots?

Answer 1

$2\left(x-\dfrac{1}{2}\right)(x-(3+\sqrt5))=\\ (2x-1)(x-3-\sqrt5)=\\ 2x^2-6x-2\sqrt5x -x+3+\sqrt5=\\ 2x^2-(7+2\sqrt5)x+3+\sqrt5$