SOLUTION: Please show how to get the roots of these functions Thank you f(x) = x^5 + x^3 + 2x - 1 g(x) = sqrt(100x^2 - 16) k(x) = (1/(x^2+5))

Algebra ->  Functions -> SOLUTION: Please show how to get the roots of these functions Thank you f(x) = x^5 + x^3 + 2x - 1 g(x) = sqrt(100x^2 - 16) k(x) = (1/(x^2+5))       Log On


   

Question 997614: Please show how to get the roots of these functions
Thank you

f(x) = x^5 + x^3 + 2x - 1
g(x) = sqrt(100x^2 - 16)
k(x) = (1/(x^2+5))
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^5+x^3+2x-1:This is a function that starts at negative infinity and ends at positive infinity. It has to have an odd number of roots in order to end up where it does.
It has no integer roots, because dividing by (x-1) or (x+1) leaves a remainder.
This root has to be found by graphing. It is not 1/2, although it is close to it. The fraction 4/9 is close but not correct either. It is about 0.446.
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sqrt (100x^2-16)=0. It cannot be negative.
square both sides
100x^2-16=0
(10x-4)(10x+4)=0
x=+/- (2/5). These have to be checked, but in both instances, the square of x is (4/25) and that *100 is 16.
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(1/(x^2+5))
It is always positive.
No value of x will make y=0. It is asymptotic.