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

1. Hayleymeyer

lets take t=x^2

2. welshfella

its degree 4 so how many roots will there be?

3. anonymous

4

4. Hayleymeyer

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

5. welshfella

yea

6. Hayleymeyer

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

7. welshfella

- which can be factored

8. welshfella

no need this can be factored

9. Hayleymeyer

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

10. Hayleymeyer

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

11. anonymous

ok

12. Hayleymeyer

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- $x=\sqrt{t}$?

13. anonymous

idk to be honest

14. welshfella

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

15. Hayleymeyer

ok well can the square of any number be negative ?

16. welshfella

now the square roots of -25 are imaginary do you know what they are?

17. welshfella

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

18. anonymous

5i?

19. welshfella

so sqrt -15 = -5i and 5 i

20. welshfella

*sqrt -25

21. welshfella

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

22. Hayleymeyer

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 :)

23. welshfella

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

24. anonymous

i have i know what they are...somewhat

25. welshfella

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

26. welshfella

Hayleymeyer obviously hasn't been taught them yet.