How to write a polynomial function with the roots 1-2i and 1+2i

f(x) = x²- 2x +5

Step-by-step explanation:

- The difference of squares identity can be written:

a² - b² = ( a -  b ) ( a + b )

Use this with a = ( x − 1 ) and b = 2 i as follows:

f(x) = ( x − 1 − 2i ) ( x − 1 + 2i )

= ( ( x − 1 ) − 2i ) ( ( x − 1 ) + 2i )

= ( x − 1 )² − ( 2i )²

= x² − 2x + 1 + 4

f(x) = x²- 2x +5

Any polynomial in x with these zeros will be a multiple (scalar or polynomial) of this f ( x )

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?