+0

# polynomial

0
57
1

Find the monic quartic polynomial f(x) with rational coefficients whose roots include x = 2 - sqrt(2) and x = 3 + sqrt(6).

Sep 18, 2020

#1
+31093
+2

This will be $$f(x) = (x-2-\sqrt2)(x-2+\sqrt2)(x-3-\sqrt6)(x-3+\sqrt6)$$

I'll leave you to multiply it out to confirm that it does indeed have rational coefficients.

Edit:  corrected signs.  Thanks to EP for making me aware of this.

Sep 18, 2020
edited by Alan  Sep 18, 2020