20. Quadratic Equations

The whole of this topic is in the range grade B to grade A*. I sus­pect that the mere men­tion of “qua­dratic equa­tions” is enough to put off many peo­ple. There is no doubt that some of the equa­tions look scary but if you work through them and prac­tice them, you’ll see that there’s no need to be afraid.

A qua­dratic expres­sion is where the high­est power of x is x².

Exam­ples of qua­dratic expressions:-

4x² + 3x + 7             x² — 4x — 3                 6x² +9             16x² — 4x

There are cer­tain types of expres­sion which are one square num­ber sub­tracted from another square num­ber. Note in the fol­low­ing exam­ples all the num­bers are square numbers:-

x² — 9                    a² — 25                  16c² — 36

Where you have this type of expres­sion in the form a² — b², where a and b are either num­bers or alge­braic terms, it’s known as the dif­fer­ence of two squares.

You need to remem­ber that a² — b² = (a — b)(a + b)

Check:  (a-b)(a + b) = a² + ab — ba — b² = a² — b²

Fac­tor­ize x² — 16

x² — 16  =  x² — 4²  = (x — 4)(x + 4)

Fac­toris­ing qua­drat­ics x² + bx + c

to be continued…

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