1. Reducible to Quadratics
Mathematic
(Preliminary)
Quadratics
Equations
Reducible to Quadratics
Stage 6 - Year 11
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2. 9.8 Equations reducible to Quadratics
Type 1
x = 3 2 x
P = 2x2
S = –3x
F = –1x x –2 x
x2 + 2 = 3x
x2 – 3x + 2 = 0
x2 – 1x – 2x + 2 = 0
(x2 – 1x) + (– 2x + 2) = 0
x(x – 1) –2 (x – 1) = 0
x = 1, x = 2
(x – 1) (x – 2) = 0

3. 9.8 Equations reducible to Quadratics
Type 2
(x + 2)2 – 3(x + 2) – 4 = 0
Let u = x + 2
u2 – 3u – 4 = 0
P = –4u2
S = –3u
F = 1u x – 4u
u2 + 1u – 4u – 4 = 0
u(u + 1) – 4(u + 1) = 0
(u + 1)( u – 4) = 0
(x )(x + 2 – 4) = 0
x + 3 = 0
x – 2 = 0
x = – 3
x = 2