Page 34 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 2 Fungsi Kuadratik

(b) Rajah di sebelah menunjukkan segi tiga PQR dengan luas kawasan berlorek (2x + 1) m
2
ialah 20 m . Cari nilai x. P Q
The diagram shows a triangle PQR with the area of the shaded region is 20 m . Find the value of x.
2
2x m
1 (2x)(2x + 1) = 20
2 R
2x + x – 20 = 0
2
x = –1 ±1 – 4(2)(–20)
2(2)

= –1 ±161
4
= 2.922, –3.422
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Maka, / Thus, x = 2.922

4. Bentukkan persamaan kuadratik dengan punca-punca yang diberikan. SP 2.1.2 TP2
Form a quadratic equation with the given roots.

(a) 4 dan / and –6 (b) –3 dan / and –5
–3 dan / and 7

Hasil tambah punca / Sum of roots Hasil tambah punca / Sum of roots
Hasil tambah punca / Sum of roots = 4 + (–6) = –2 = (–3) + (–5) = –8
= –3 + 7 = 4
Hasil darab punca / Product of roots Hasil darab punca / Product of roots
Hasil darab punca / Product of roots = (4)(–6) = –24 = (–3)(–5) = 15
= (–3)(7) = –21
2
2
∴ x – 4x – 21 = 0 ∴ x + 2x – 24 = 0 ∴ x + 8x + 15 = 0
2
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(c) –2 dan / and 1 (d) 1 dan / and 2 (e) 1 dan / and 2
3 2 4
Hasil tambah punca / Sum of roots Hasil tambah punca / Sum of roots Hasil tambah punca / Sum of roots
2
1
1
1
= –2 + = – 5 = + = 9 = + 2 = 9
3 3 2 5 10 4 4
Hasil darab punca / Product of roots Hasil darab punca / Product of roots Hasil darab punca / Product of roots
1
2
1 2
1
1
= (–2)   = – =    = =   (2) = 1
2 5
2
5
4
3
3
9
1
5
2
1
∴ x + x – = 0 ∴ x – 9 x + = 0 ∴ x – x + = 0
2
2
2
3 3 10 5 4 2
2
3x + 5x – 2 = 0 10x – 9x + 2 = 0 4x – 9x + 2 = 0
2
2
5. Selesaikan setiap yang berikut. SP 2.1.2 TP4
Solve each of the following.
Punca-punca persamaan kuadratik x – 4x + 2 = 0 ialah α dan β, bentukkan persamaan kuadratik dengan
2
2
2
punca-punca α dan β .
The roots of quadratic equation x – 4x + 2 = 0 are α and β, form a quadratic equation with the roots of α and β .
2
2
2
a = 1, b = –4, c = 2 Hasil darab punca / Product of roots:
b
2 2
α + β = – = – (–4) = 4 = α β
a 1 = (αβ) 2 Tip Penting
c
2
αβ = = = 2 = 2 2 (i) (a + b) = a + 2ab + b 2
2
2
a 1 = 4 (ii) (a – b) = a – 2ab + b 2
2
2
2
2
Hasil tambah punca / Sum of roots: Persamaan kudratik (iii) a – b = (a + b)(a – b)
(iv) a + b = (a + b) – 2ab
2
2
2
2
2
2
α + β = (α + β) – 2αβ Quadratic equation:
= 4 – 2(2) x − 12x + 4 = 0
2
2
= 12
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