Mathematics for Chemistry/Functions

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Functions as tools in chemistry[edit]

The quadratic formula[edit]

In order to find the solutions to the general form of a quadratic equation,

a x^{2 }+ b x + c = 0

there is a formula

 x =  \frac {-b \pm  \sqrt { (b^{2 }- 4 a c)} } {2 a}

(Notice the line over the square root has the same priority as a bracket. Of course we all know by now that \sqrt {a +b} is not equal to \sqrt {a } + \sqrt {b} but errors of priority are among the most common algebra errors in practice).

There is a formula for a cubic equation but it is rather complicated and unlikely to be required for undergraduate-level study of chemistry. Cubic and higher equations occur often in chemistry, but if they do not factorise they are usually solved by computer.

Solve:

 2x^{2} -  14 x + 9

 1.56 ( x^{2} +  3.67 x + 0.014 )

Notice the scope or range of the bracket.

 2x^{2 } -  4 x + 2

 -45.1 ( 1.2[A]^{2 } -  57.9 [A] + 4.193 )

Notice here that the variable is a concentration, not the ubiquitous x.