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

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.1its degree 4 so how many roots will there be?

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1so we have the equation t^2 +21t100 =0

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1Looking at the discriminant we have discriminant = \[\frac{ 21\pm \sqrt{21^24(1)(100)} }{ 2}\]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1 which can be factored

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1no need this can be factored

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1simplifying the discriminant we get  t=4 or t= 25

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1we know that x^2 =t so \[x=\sqrt{t}\]

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1we 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 \[x=\sqrt{t}\]?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1t = 4 gives 2 values for x 2 and  2

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1ok well can the square of any number be negative ?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1now the square roots of 25 are imaginary do you know what they are?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1yes  you introduce the operator i which stands for the square root of 1.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1so sqrt 15 = 5i and 5 i

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1and theres your 4 roots 2, 2 , 5i and 5i

Hayleymeyer
 one year ago
Best ResponseYou've already chosen the best response.1well \[\sqrt{25} \] 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 :)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1probably you haven't come to complex and imaginary numbers yet. They are not real numbers but they do exist in math.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have i know what they are...somewhat

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1Yes  mathematicians introduced them because some problems could not be solved using real numbers alone.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1Hayleymeyer obviously hasn't been taught them yet.
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