+1836 Find a monic quartic polynomial f(x) with rational coefficients whose roots include x=3-isqrt[4]2. <- it's supposed to look like the four is an exponent after the i. So, 3-i^4 sqrt2. Give your answer in expanded form.
+23252 If 3 - i4sqrt(2) = 3 - sqrt(2) because i4 = 1.
If 3 - sqrt(2) is a root then (if the coefficients are rational), 3 + sqrt(2) is also a root.
If it's a quartic, you will have 2 more roots. They will be two rational roots [such as 2/3 and -7], or a pair of conjugate complex roots [such as 2 + 3i and 2 - 3i], or a pair of conjugate irrational roots [such as -5 + sqrt(19) and -5 - sqrt(19)].
(x - (3 - sqrt(2) ) · (x - (3 + sqrt(2)) · ( x - (something) ) · ( x - (something) = 0
+23252 If 3 - i4sqrt(2) = 3 - sqrt(2) because i4 = 1.
If 3 - sqrt(2) is a root then (if the coefficients are rational), 3 + sqrt(2) is also a root.
If it's a quartic, you will have 2 more roots. They will be two rational roots [such as 2/3 and -7], or a pair of conjugate complex roots [such as 2 + 3i and 2 - 3i], or a pair of conjugate irrational roots [such as -5 + sqrt(19) and -5 - sqrt(19)].
(x - (3 - sqrt(2) ) · (x - (3 + sqrt(2)) · ( x - (something) ) · ( x - (something) = 0
