Page 35 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 2 Fungsi Kuadratik

(a) Punca-punca persamaan kuadratik 6x + 2x – 1 = 0 ialah α dan β. Bentukkan persamaan kudartik dengan
2
punca-punca berikut.
The roots of quadratic equation 6x + 2x – 1 = 0 are α and β. Form a quadratic equation with the following roots.
2
2
2
(i) 1 dan / and 1 (ii) 2α + 1 dan / and 2β + 1 (iii) 2α dan / and 2β
α β
a = 6, b = 2, c = –1 Hasil tambah punca: Hasil tambah punca:
Sum of roots:
Sum of roots:
2
b
α + β = – = – = – 1 (2α + 1) + (2β + 1) = 2α + 2β 2
2
a 6 3 = 2(α + β) + 2 = 2(α + β )
2
2
c
αβ = = – 1 1 = 2[(α + β) – 2αβ]
2
 
a 6 = 2 – + 2 1 2 1
3
 
 
Hasil tambah punca: = 4 = 2 – 3 – 2 – 6
Sum of roots: 3 8
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1 + Hasil darab punca: = 9 Tip Penting
1
α β Product of roots: α + β = (α + β) − 2αβ
2
2
2
= α + β (2α + 1)(2β + 1)
αβ = 4αβ + 2(α + β) + 1 Hasil darab punca:
Product of roots:
1
1
   
– 1 = 4 – + 2 – + 1 = 2α (2β )
2
2
= 3 6 3 = 4(αβ) 2
– 1 = – 1 1 2
 
6 3 = 4 –
= 2 4 1 6
∴ x – x – = 0 = 1
2
Hasil darab punca: 3 3 9
2
Product of roots: 3x – 4x – 1 = 0 8 1
2
1 × = 1 = –6 ∴ x – x + = 0
1
9
9
α β αβ 9x – 8x + 1 = 0
2
∴ x – 2x – 6 = 0
2
6. Tentukan julat nilai x yang memuaskan setiap ketaksamaan kuadratik berikut. SP 2.1.3 TP4
Determine the range of values of x that satisfies each of the following quadratic inequalities.
(i) (x – 2)(x + 4)  0 (ii) (2x – 1)(x + 5)  0
Menggunakan kaedah lakaran graf: Apabila / When (2x – 1)(x + 5) = 0,
Using sketching graph method: 1
Apabila / When (x − 2)(x + 4) = 0, x = , x = –5
2
x = 2, x = −4 Oleh kerana, (2x – 1)(x + 5)  0, x berada di
Oleh kerana (x – 2)(x + 4)  0, x berada bawah paksi-x.
di atas paksi-x. Since (2x – 1)(x + 5)  0, x lies below the x-axis.
Since (x – 2)(x + 4)  0, x lies above the x-axis. y
y x
–5 0 1
– 2
–5
+ + x
–4 0 2
1
–8 Maka, julat bagi nilai x ialah −5  x  .
2
1
Maka, julat bagi nilai x ialah x  −4 atau x  2. Thus, the range of values of x is −5  x  .
2
Thus, the range of values of x is x  −4 or x  2.
Tip Penting
Kewujudan "sama dengan" pada simbol
Menggunakan kaedah garis ketaksamaan bagi julat x ditentukan mengikut
nombor dan jadual ketaksamaan kuadratik yang diberikan.
Using methods of number line The existence of "equal to" in the inequality symbol for
and table
the range of x is determined according to the quadratic
inequalities given.

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