Question

Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.

Answer 1

lets take t=x^2

Answer 2

its degree 4 so how many roots will there be?

Answer 3

4

Answer 4

so we have the equation
t^2 +21t-100 =0

Answer 5

yea

Answer 6

Looking at the discriminant
we have discriminant = \[\frac{ -21\pm \sqrt{21^2-4(1)(-100)} }{ 2}\]

Answer 7

- which can be factored

Answer 8

no need this can be factored

Answer 9

simplifying the discriminant we get -
t=4 or t= -25

Answer 10

we know that
x^2 =t
so
\[x=\sqrt{t}\]

Answer 11

ok

Answer 12

we have 2 values of t :)
one is positive and one is negative :)
what do u think can we put negative value of t in this function to get x- \[x=\sqrt{t}\]?

Answer 13

idk to be honest

Answer 14

t = 4 gives 2 values for x
2 and - 2

Answer 15

ok well can the square of any number be negative ?

Answer 16

now the square roots of -25 are imaginary

do you know what they are?

Answer 17

yes - you introduce the operator i which stands for the square root of -1.

Answer 18

5i?

Answer 19

so sqrt -15 = -5i and 5 i

Answer 20

*sqrt -25

Answer 21

and theres your 4 roots 2, -2 , 5i and -5i

Answer 22

well \[\sqrt{-25} \] does not exists cause -25 is negative so we r left with t=4

puttin t=4 in the equation \[x=\sqrt{t}\]we get x=2 and x=-2 :)

Answer 23

probably you haven't come to complex and imaginary numbers yet. They are not real numbers but they do exist in math.

Answer 24

i have i know what they are...somewhat

Answer 25

Yes - mathematicians introduced them because some problems could not be solved using real numbers alone.

Answer 26

Hayleymeyer obviously hasn't been taught them yet.