Page 37 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 2 Fungsi Kuadratik

PBD 2.2 Jenis-jenis Punca Persamaan Kuadratik Buku Teks
PBD
PBD
Types of Roots of Quadratic Equations ms. 45 – 48
FOKUS TOPIK

1. Jenis-jenis punca persamaan kuadratik ditentukan oleh nilai pembezalayan, b − 4ac.
2
2
The types of roots of quadratic equations are determined by the value of discriminant, b − 4ac.
Jenis-jenis punca
Types of roots
Dua punca nyata Tiada punca nyata / No real roots
Two real roots b − 4ac  0 Jenis-jenis punca
2
Find the discriminant and determine the type of roots of each of the following quadratic equations. Reserved

Types of roots of
b − 4ac  0
b − 4ac = 0
2
2
Berbeza / Different Sama / Equal persamaan kuadratik
quadratic equations
VIDEO
7. Cari nilai pembezalayan dan tentukan jenis punca bagi setiap persamaan kuadratik berikut. TP1 TP2
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SP 2.2.1
(a) x = 2(x – 5) (b) 5x – 4x = 5
2
2
2
x = 3x – 1
x = 2x – 10 5x – 4x – 5 = 0
2
2
x – 3x + 1 = 0 x – 2x + 10 = 0
2
2
2
2
b – 4ac = (–3) – 4(1)(1) b – 4ac = (–4) – 4(5)(–5)
2
2
2
2
= 5  0 b – 4ac = (–2) – 4(1)(10) = 116  0
= –36  0
Mempunyai dua punca nyata Mempunyai dua punca nyata
dan berbeza. Tidak mempunyai punca nyata. dan berbeza.
Has two real and different roots. Has no real roots. Has two real and different roots.
(c) –3x – 7x = –6 (d) 9x – 12x + 4 = 0 (e) 3x = 7(x – 5)
2
2
2
–3x – 7x + 6 = 0 b – 4ac = (–12) – 4(9)(4) 3x = 7x – 35
2
2
2
2
= 0 3x – 7x + 35 = 0
2
b – 4ac = (–7) – 4(–3)(6)
2
2
= 121  0 Mempunyai dua punca nyata b – 4ac = (–7) – 4(3)(35)
2
2
dan sama. = –371  0
Mempunyai dua punca nyata dan Has two equal real roots.
berbeza. Tidak mempunyai punca nyata.
Has two real and different roots. Has no real roots.
8. Selesaikan setiap yang berikut. SP 2.2.2 TP3
Solve each of the following.
(a) Persamaan kuadratik 4x + px = –p, dengan p
2
Persamaan kuadratik kx + kx + 3 = 0, dengan k ialah pemalar, tidak mempunyai punca yang
2
ialah pemalar, mempunyai dua punca sama. Cari nyata. Cari julat bagi p.
nilai-nilai yang mungkin bagi k. The quadratic equation 4x + px = –p, where p is a constant,
2
The quadratic equation kx + kx + 3 = 0, where k is a constant, has no real roots. Find the range of values of p.
2
has two equal roots. Find the possible values of k.
4x + px = –p
2
b – 4ac = 0 4x + px + p = 0
2
2
k – 4(k)(3) = 0
2
2
k – 12k = 0 b – 4ac  0 + – + p
2
2
k(k – 12) = 0 p – 4(4)(p)  0 0 16
2
k = 0, k = 12 p – 16p  0
p(p – 16)  0
∴ 0  p  16
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