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

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right