Page 10 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

Solution
2
x – 2x – 8 = 0 New SOR: 2α + 2β = 2(α + β)
b
α + β = – = 2(2)
a
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= – (–2) = 4
1 New POR: (2α)(2β) = 4αβ
= 2 = 4(–8)
αβ = c TIPS = –32
a
= –8 Sum of roots, α + β = − b a The new quadratic equation is Form 4
2
1 c x – (2α + 2β)x + (2α)(2β) = 0
= –8 Product of roots, αβ = a x – 4x + (–32) = 0
2
x – 4x – 32 = 0
2

Example 5
Find the range of values of x for each of Table method
the following quadratic inequalities using Range of values of x
the method of graph sketching, number
line or table. x  –4 –4  x  3 x  3
(a) x + x – 12  0 (x – 3) – – +
2
(b) (2 – 3x)(x + 5)  x + 25 (x + 4) – + +
(x – 3)(x + 4) + – +
Solution
The range of values of x is < –4 and
(a) x + x – 12 > 0 x > 3.
2
Graph sketching method
Let x + x – 12 = 0 (b) (2 – 3x)(x + 5)  x + 25
2
2
(x – 3)(x + 4) = 0 –3x – 13x + 10  x + 25
2
x = 3 or x = –4 –3x – 14x – 15  0
y (–3x – 5)(x + 3)  0
+ + x Graph sketching method
–4 – 0 3 Let (–3x – 5)(x + 3) = 0
5
x = – or x = –3
3
The range of values of x is < –4 and
x > 3.
Number line method + x
– –3 5 –
x = –5, x = 0, x = 4, – 3
(–5 – 3)(–5 + 4) > 0 (0 – 3)(0 + 4) < 0 (4 – 3)(4 + 4) > 0
5
The range of values of x is –3  x  – .
x 3
+ –4 – 3 +
The range of values of x is < –4 and
x > 3.

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