For the polynomial function ƒ(x) = −x6 + 3x4 + 4x2, find the zeros. then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.

There is a multiple zero at 0 (which means that it touches there), and there are single zeros at -2 and 2 (which means that they cross). There is also 2 imaginary zeros at i and -i.

You can find this by factoring. Start by pulling out the greatest common factor, which in this case is -x^2.

-x^6 + 3x^4 + 4x^2

-x^2(x^4 - 3x^2 - 4)

Now we can factor the inside of the parenthesis. You do this by finding factors of the last number that add up to the middle number.

-x^2(x^4 - 3x^2 - 4)

-x^2(x^2 - 4)(x^2 + 1)

Now we can use the factors of two perfect squares rule to factor the middle parenthesis.

-x^2(x^2 - 4)(x^2 + 1)

-x^2(x - 2)(x + 2)(x^2 + 1)

We would also want to split the term in the front.

-x^2(x - 2)(x + 2)(x^2 + 1)

(x)(-x)(x - 2)(x + 2)(x^2 + 1)

Now we would set each portion equal to 0 and solve.

First root

x = 0 ---> no work needed

Second root

-x = 0 ---> divide by -1

x = 0

Third root

x - 2 = 0

x = 2

Forth root

x + 2 = 0

x = -2

Fifth and Sixth roots

x^2 + 1 = 0

x^2 = -1

x = +/-

x = +/- i

560

hope this : )

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all