Mathematics for Chemistry/Functions

The quadratic formula
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 $$x$$.