SOLUTION: Find all exact zeros (both real and complex) of the function: f x = 4x^4 - 21x^2

SOLUTION: Find all exact zeros (both real and complex) of the function: f x = 4x^4 - 21x^2 - 25.

Question 249121: Find all exact zeros (both real and complex) of the function:
f x = 4x^4 - 21x^2 - 25.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
4x^4 - 21x^2 - 25=0
4*-25=-100
4 & -25 are factors of -100 whose sum is -21
4x^4+4x^2-25x^2-25=0
4x^2(x^2+1)-25(x^2+1)=0 factor by grouping
(4x^2-25)(x^2+1)=0
(2x+5)(2x-5)(x^2+1)=0
2x=-5, x=-5/2
2x=5, x=5/2
x^2=-1, x=sqrt(-1), x=i
x=-sqrt(-1), x=-i
.
Ed
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