HP 35s User Manual

 
 
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HP 35s  Roots of polynomials 
 
 
 
 
Polynomials 
 
Roots of a polynomial 
 
Using the SOLVE function 
 
Practice solving for roots of polynomials 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   

 
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HP 35s  Roots of polynomials 
 
hp calculators - 2 - HP 35s  Roots of polynomials - Version 1.0 
Polynomials 
 
A polynomial is an expression containing one or more terms called monomials. These terms contain one or more 
variables multiplied by a constant coefficient. Each of these variables will have a positive exponent. A term may have an 
exponent of zero, in which case it is a constant term. A polynomial will generally not contain negative exponents or 
division by a term or...

 
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HP 35s  Roots of polynomials 
 
hp calculators - 3 - HP 35s  Roots of polynomials - Version 1.0 
 In RPN or algebraic mode:  ),)-$./
//012$345412$564/
//7/
 
 Figure 1 
 
 To show the checksum and length of this program, press the following in RPN or algebraic mode. Note that 
the symbol &/means to press the right arrow direction of the cursor key. 
/
/In RPN or algebraic mode: %&8  
 Figure 2 
 
 If the checksum of the program just entered does not equal 8BFA, then you have not...

 
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HP 35s  Roots of polynomials 
 
hp calculators - 4 - HP 35s  Roots of polynomials - Version 1.0 
 The same root is returned. This is a good indication (but certainly not foolproof) that there are no roots 
larger than +2 for this equation. 
 
 To see if there is a root less than +2 for this equation, store a new guess for X of –10 into the variable X. 
Then solve for the value of X.  
 
 In RPN or algebraic mode:  69;):$)!$/
 
 Figure 5 
 
Answer: Roots found for the equation are –1.5...

 
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HP 35s  Roots of polynomials 
 
hp calculators - 5 - HP 35s  Roots of polynomials - Version 1.0 
 
 Then, to exit the program environment, press:), 
 
 Store an initial guess for X of 10 into the variable X. Then set the function to X and solve for the value of X.  
 
 In RPN or algebraic mode:  69):$#$)!$/
 
 Figure 8 
 
 Since you feel this equation might have a root larger than this, store a new guess for X of 100 into the 
variable X. There is no need to set the function to X...

 
 
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HP 35s  Advanced uses of logarithmic functions 
 
 
 
 
Log and antilog functions 
 
Practice using log and antilog functions 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   

 
hp calculators 
 
HP 35s  Advanced uses of logarithmic functions 
 
hp calculators - 2 - HP 35s  Advanced uses of logarithmic functions - Version 1.0 
Log and antilog functions 
 
Before calculators like the HP 35s became easily available, logarithms were commonly used to simply multiplication. 
They are still used in many subjects, to represent large numbers, as the results of integration, and even in number 
theory. 
 
The HP 35s has four functions for calculations with logarithms. These are the...

 
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HP 35s  Advanced uses of logarithmic functions 
 
hp calculators - 3 - HP 35s  Advanced uses of logarithmic functions - Version 1.0 
Example 2: A rare species of tree has a trunk whose cross-section changes as 1/x with the height x. (Obviously this 
breaks down at ground level and at the tree top.) The cross section for any such tree is given by A/x, where 
A is the cross-section calculated at 1 meter above the ground. What is the volume of the trunk between 1 
meter and 2 meters...

 
hp calculators 
 
HP 35s  Advanced uses of logarithmic functions 
 
hp calculators - 4 - HP 35s  Advanced uses of logarithmic functions - Version 1.0 
 Figure 5 
 
Answer: The log to base 3 of 5 is 1.465 within the current accuracy setting of the calculator, as shown by Figure 5. 
Calculating 3 to this power gives 5.000 which confirms that the correct value for the log had been obtained.  
 
Example 4: An activity of 200 is measured for a standard of Cr51 (with a half-life of 667.20 hours). How much...