Page 9 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

(b) –2x – 7x + 5 = 0 Solution
2
7

–2 x + x – 5  = 0 (a) Sum of roots (SOR) = 4 + (–7)
2
2
2
7
x + x = 5 = –3
2
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2 2 Product of roots (POR) = 4 × (–7)
= –28
7
5
7
7
x + x +   2 = +   2 The quadratic equation is
2
2
4
4
2
Form 4  x + 7  2 = 89 x – (SOR)x + (POR) = 0
2
x – (–3)x + (–28) = 0
2
4
16
2
89
7
x + = ±  x + 3x – 28 = 0
4 16 (b) Sum of roots (SOR)
x = 0.6085 or x = –4.1085 1 3 13
 
= – + – = –
2 7 14
Example 2 Product of roots (POR)
3
1
3
 
Solve the equation –7x – 6x + 8 = 0 using = – × – = 14
2
7
2
the formula: The quadratic equation is
ac
–b ± 2
b
– 4
2
x = 2a x – (SOR)x + (POR) = 0

x – – 13  x + 3 = 0
2
Solution 14 14
14x + 13x + 3 = 0
2
a = –7, b = –6, c = 8
(–6)
–(–6) ± – 4(–7)(8)
2
x = 2(–7)
260
6 ± Alternative Method
x =
–14 (a) (x – α)(x – β) = 0
260
260
6 –  6 +  (x – 4)[x – (–7)] = 0
x = or x = (x – 4)(x + 7) = 0
–14 –14 x + 3x – 28 = 0
2
x = 0.7232 or x = –1.5803 (b) (x – α)(x – β) = 0
1
3
      = 0
x – –
x – –
2
7
 x + 1  x + 3  = 0
2
7
Checking answers using 13 3
2
calculator x + 14 x + 14 = 0
INFO 14x + 13x + 3 = 0
2
Example 3 Example 4
Form a quadratic equation using the given
roots. Given α and β are the roots of quadratic
2
(a) 4 and –7 equation x – 2x – 8 = 0. Form a quadratic
1
3
(b) – and – equation that has the roots 2α and 2β.
2 7
16
02 Ranger Add Mathematics Tg4.indd 16 25/02/2022 9:10 AM