GB-19-01-001 · Factorising quadratic equations

Solve $x^{2} + 4x - 5=0$ .

Solving Equations: Quadratics by Factorising (a = 1) Booklet p. 5 & p. 12

Method

1) Rearrange = 0

2) Factorise using ac and 2×2 grid

3) Put each bracket = 0 and solve

Worked Example (GB-19-01-001)

2) Factorise using 2×2 Grid & a×c T-table (Booklet p. 5–6):

×	$x$	$-1$
$x$	$x^2$	$-x$
$+5$	$+5x$	$-5$

a \times c = 1 \times (-5) = -5

-1

+5

c is negative so signs are different (+ and −)...

-1 + 5 = +4

✔

\text{Brackets: } \mathbf{(x + 5)(x - 1)}

3) Put each bracket = 0 and solve (Booklet p. 12):

x + 5 = 0

-5

-5

\mathbf{x = -5}

x - 1 = 0

+1

+1

\mathbf{x = 1}

x=1

x=-5