Page 4 - TOP ONE ADDMATHS TG4

Additional Mathematics Form 4 Chapter 2 Quadratic Functions

2. Solve the following quadratic equations by using the formula method. Give your answers correct to four
decimal places. PL 3
Selesaikan persamaan kuadratik berikut dengan menggunakan kaedah rumus. Berikan jawapan anda betul kepada empat tempat
perpuluhan.
Example (a) 2x – 5x – 9 = 0
2
2
x – 6x + 7 = 0
a = 2, b = –5, c = –9
a = 1, b = –6, c = 7 –(–5) ± 
(–5) – 4(2)(–9)
2
(–6) ±  x = 2(2)
(–6) – 4(1)(7)
2
x = –  B
2(1) = 5 ± 97

6 ± 8 4
=


2 x = 5 + 97 or x = 5 – 97


6 + 8 6 – 8 4 4
x = or x = = 3.7122 = –1.2122
2 2
= 4.4142 = 1.5858
2
2
(b) 3x – 5x + 1 = 0 (c) –x + 8x – 9 = 0
a = 3, b = –5, c = 1 a = –1, b = 8, c = –9
–(–5) ±  –8 ± 
(–5) – 4(3)(1)
2
2
x = x = (8) – 4(–1)(–9)
2(3) 2(–1)


= 5 ± 13 = –8 ± 28
6 –2


5 + 13 5 – 13  
x = or x = x = –8 + 28 or x = –8 – 28
6 6 –2 –2
= 1.4343 = 0.2324 = 1.3542 = 6.6458
3. Solve the following problems. PL 4
Selesaikan masalah-masalah berikut. (2x + 3) cm
(a) The product of 3x and (x + 2) is (–x + 12). Find (b)
the values of x. Give your answers correct to
three decimal places. A x cm B (2x + 3) cm
Hasil tambah 3x dan (x + 2) ialah (–x + 12). Cari nilai-
nilai x. Berikan jawapan anda betul kepada tiga tempat The diagram shows two squares, A and B. If the
perpuluhan. area of the square A is equal to the perimeter
3x(x + 2) = –x + 12 of the square B, find the value of x. Give your
2
3x + 6x = –x + 12 answer correct to three significant figures.
3x + 7x – 12 = 0 Rajah di atas menunjukkan dua buah segi empat sama,
2
A dan B. Jika luas segi empat sama A bersamaan dengan
7
x + x – 4 = 0 perimeter segi empat sama B, cari nilai x. Berikan jawapan
2
3
7
x + x = 4 anda betul kepada tiga angka bererti.
2
3 2
x + x +   2 = 4 +   2 x = 4(2x + 3)
7
7
x = 8x + 12
2
3
3
7
2
3 2 2 x – 8x – 12 = 0
2
2
7
7
7
x + x +   2 = 4 +   2 x = –(–8) ± √(–8) – 4(1)(–12)
2
3 6 6 2(1)
8 ± √112
2
 x + 7  = 193 = 2
36
6
7
x + = ± 193 x = 8 + √112 or x = 8 – √112
6 36 2 2
x = 1.149 or x = –3.482 = 9.29 = –1.29 (rejected)
∴ x = 9.29
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