document.write( "Question 997614: Please show how to get the roots of these functions
\n" ); document.write( "Thank you\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "f(x) = x^5 + x^3 + 2x - 1 \r
\n" ); document.write( "\n" ); document.write( "g(x) = sqrt(100x^2 - 16) \r
\n" ); document.write( "\n" ); document.write( "k(x) = (1/(x^2+5)) \n" ); document.write( "
Algebra.Com's Answer #615637 by Boreal(15235)\"\" \"About 
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.
\n" ); document.write( "It has no integer roots, because dividing by (x-1) or (x+1) leaves a remainder.
\n" ); document.write( "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.
\n" ); document.write( "=====================
\n" ); document.write( "sqrt (100x^2-16)=0. It cannot be negative.
\n" ); document.write( "square both sides
\n" ); document.write( "100x^2-16=0
\n" ); document.write( "(10x-4)(10x+4)=0
\n" ); document.write( "x=+/- (2/5). These have to be checked, but in both instances, the square of x is (4/25) and that *100 is 16.
\n" ); document.write( "==============
\n" ); document.write( "(1/(x^2+5))
\n" ); document.write( "It is always positive.
\n" ); document.write( "No value of x will make y=0. It is asymptotic.
\n" ); document.write( " \n" ); document.write( "
\n" );