+284 Hi can someone help me with this problem?
Find a monic quartic polynomial f(x) with rational coefficients whose roots include \(x=1-\sqrt 2\) and \(x=2+\sqrt 5\). Give your answer in expanded form.
Thanks!
+1223 If a polynomial has a root of the form \(a + \sqrt{b}\) then it must also have another root of the form \(a - \sqrt{b}.\)
So, our quartic is:
\((x - (1 - \sqrt{2}))(x - (1 + \sqrt{2}))(x - (2 + \sqrt{5}))(x - (2 - \sqrt{5}))\)
