+77 Please halp asap! Find a monic quartic polynomial with rational coefficients whose roots include 2+sqrt5 and 1-sqrt2 . Give your answer in expanded form.
+23246 Since 2 + sqrt(5) is a root 2 - sqrt(5) is also a root.
This means that [ x - (2 + sqrt(5)) ] and [ x - (2 - sqrt(5)) ] are factors.
Multiplying these factors together gives you x2 - 4x - 1.
Since 1 - sqrt(2) is a root 1 + sqrt(2) is also a root.
This means that [ x - (1 - sqrt(2)) ] and [ x - (1 + sqrt(2)) ] are factors.
Multiplying these factors together gives you x2 - 2x - 1.
Multiplying x2 - 4x - 1 and x2 - 2x - 1 together gives you x4 - 6x3 + 6x2 + 6x + 1.
