Find a monic quartic polynomial f (x) with rational coefficents whose roots include

x=1-sqrt2, and x=2+sqrt5. Give your answer in expanded form.

The polynomial hose roots are:

x = 1 - √2 and

x = 2 + √5

Is

x² - (3 + √5 + √2) x + 2 + √5 - 2√2 - √10 = 0

Step-by-step explanation:

The roots of the equation are

x = 1 - √2 and

x = 2 + √5

(x - 1 + √2) (x - 2 - √5) = 0

x² - 2x - x√5 - x + 2 + √5 + x√2 - 2√2 - √10 = 0

x² - (3 + √5 + √2) x + 2 + √5 - 2√2 - √10 = 0

This is the expanded form