+0

Intermediate Algebra

0
49
2
+282

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!

Feb 25, 2021

#1
+939
+2

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:

$$(x - (1 - \sqrt{2}))(x - (1 + \sqrt{2}))(x - (2 + \sqrt{5}))(x - (2 - \sqrt{5}))$$

Feb 25, 2021
#2
+282
0

Thank you so much!

Caffeine  Feb 26, 2021