Page 6 - TOP ONE ADDMATHS TG4

Additional Mathematics Form 4 Chapter 2 Quadratic Functions

2
(a) If the roots of the quadratic equation x – 4x – 5 = 0 are a and b, form new quadratic equations using
the roots
Jika punca-punca bagi persamaan kuadratik x – 4x – 5 = 0 ialah a dan b, bentukkan persamaan kuadratik baru menggunakan
2
punca-punca
1
(i) 1 and / dan (ii) (a + b) only / sahaja
2
a b
x – 4x – 5 = 0 (i) Sum of roots: (ii) Sum of roots:
2
2
1
1 + = b + a (a + b) + (a + b) 2
b a b ab = 4 + 4 2
2
a + b = –
a = – 4 = 32
= 4 5
c Product of roots: Product of roots:
ab = 1 (a + b) × (a + b)
2
2
1
1
a    =
2
= –5 a b ab = 4 × 4 2
= – 1 = 256
5
x – 32x + 256 = 0
2
1

2
x – – 4  x – = 0
5
5
1
4
2
x + x – = 0
5 5
5x + 4x – 1 = 0
2
1
(b) It is given that the roots of the quadratic equation 4x – px – 4 = 0 are q and – . Find the values of
2
4
p and q.
1
Diberi punca-punca bagi persamaan kuadratik 4x – px – 4 = 0 ialah q dan – . Cari nilai-nilai p dan q.
2
4
4x – px – 4 = 0 Product of roots = –1 Sum of roots = p
2
p 1 4

x – x – 1 = 0 ∴ q –  = –1
2
4 4 1 p

q = 4 ∴ q + – 4  = 4
1
4 – = p
4 4
p
15 =
4 4
p = 15
(c) Find the possible values of k if one of the roots of the quadratic equation x – kx + 8 = 0 is twice the
2
other.
2
Cari nilai-nilai k yang mungkin jika salah satu punca bagi persamaan kuadratik x – kx + 8 = 0 adalah dua kali ganda
punca yang satu lagi.
Let the roots of the quadratic equation Sum of roots = k
x – kx + 8 = 0 be a and 2a. ∴ a + 2a = k
2
k = 3a
Product of roots = 8 k = 3(2) or k = 3(–2)
∴ 2a = 8 = 6 = –6
2
a = 4
2

a = ± 4
= 2 or –2

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02 TOP 1 + MATH F4.indd 21 20/12/2019 9:34 AM