+0

# Polynomial

0
179
1

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).

Jan 8, 2022

#1
+118117
+1

x = 1 - sqrt(2)] and x = 2 + sqrt(7).

$$f(x)=(x-(1-\sqrt2))(x-(1+\sqrt2))(x-(2-\sqrt7))(x-(2+\sqrt7))$$

That should do it.  You can expand.  Try graphing it using desmos to check it is right first ;)

Jan 8, 2022