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…