Wednesday, 4 January 2012

PERSAMAAN KUADRATIK 1

Saya suka menjelaskan lebih awal. Persamaan Kuadratik (PK) ini ada 2 bahagian utama. Saya namakan sebagai berikut :

BAHAGIAN A (2 PUNCA MEMBENTOK  1 PERSAMAAN)
KOD 2R


BAHAGIAN B (1 PERSAMAAN MENCARI 2 PUNCA)
KOD 1E

Dalam bahagian pertama ini, saya akan fokus kepada bahagian A dengan menggunakan kod 2R (maksudnya 2 ROOTS atau 2 punca).

BAHAGIAN A (2 PUNCA MEMBENTOK 1 PERSAMAAN)    KOD 2R
Q1. Given that 3 and -5 are the roots of the equation. Form the equation


TUGAS ANDA : TUKAR TANDA PADA PUNCA-PUNCA DIBERI
(X -3) (X + 5) = 0
X2 + 2X - 15 = 0

Q2. Given that -4 and 5 are the roots of the equation. Form the equation 
(x + 4) (x - 5) = 0
x2 - x - 20 = 0

Q3.  Given that -1 and -2 are the roots of the equation. Form the equation
(x + 1) (x + 2) = 0
x2 + 2x + 1x + 2 = 0
x2 + 3x + 2 = 0


BAHAGIAN B (1 PERSAMAAN MENCARI 2 PUNCA) KOD 1E 

BILA ANDA TERLIHAT SAHAJA ADA PERSAMAAN KUADRATIK DIBERIKAN, ANDA MESTI GUNAKAN KOD 1E (bermaksud 1 Equation atau 1 persamaan)

TUJUANNYA : MENCARI PUNCA ATAU ANU YANG TERSEMBUNYI.. 

Q1. Given that m and 3 are the roots for the equation x2 + 4x - k = 0. Find m and k

Daripada x2 + 4x - k = 0
a = 1, b = 4, c = -k

SUM OF ROOTS (SOR) = - b / a      [INI SYARAT UTAMA]
m + 3 = - (4/1)
m + 3 = -4
m = -7

PRODUCT OF ROOTS (POR) = c/a    [INI SYARAT UTAMA]
(m)(3) = (-k / 1)
3m = -k, maka k = -3m
= (-3)(-7) = 21

Q4. Given that 2 and -m are the roots for the equation 3x2 + kx + 11 = 0. Find m and k. 


Daripada 3x2 + kx + 11 = 0
 a = 3, b =k, c = 11

SUM OF ROOTS (SOR) = -b/a
2 + (-m)  = - b/a
2 - m = - (k / 3)
- k = 3 (2 - m) =  6 - 3m
So k = -6 + 3m  = 3m - 6    [PERSAMAAN 1]

PRODUCT OF ROOTS (POR) = c/a
 (2) (-m) = c / a
- 2m = 11 / 3
m = - 11 / 6      [PERSAMAAN 2]

Masukkan [2] ke dalam [1], k = 3m - 6
                                            k = 3 (- 11 / 6) - 6
                                            k = - 11 / 2 - 6
                                            k = - 23 / 2                                     
 
Q5. Given that m and n are the roots for the equation 3x2 - 4x + 16 = 0. Find  m and n, where n is positive.  

Daripada 3x2 - 4x + 16 = 0
a = 3, b = -4, c = 16 

SUM OF ROOTS  (SOR) = -b/a
m + n = - (-4 / 3) = 4/3
m + n = 4 / 3      [PERSAMAAN 1]

PRODUCT OF ROOTS (POR) = c/a
(m)(n) = 16 / 3   [PERSAMAAN 2]

DARIPADA [1], m = (4 / 3) - n
masukkan ke dalam [2]

[(4 / 3) - n] (n) = 16 / 3
4n / 3 - n2 - 16 / 3 = 0
- n2 + 4n / 3 - 16/3 = 0
so a = -1, b = 4/3 = 1.3333, c = -16/3 = -5.3333

Guna kalkulator,anda akan perolehi nilai n = 0.6667


Kemudian cari nilai m, m = (4/3) - 0.6667
so m = 0.6666.

SEKIRANYA ANDA INGIN MEMBERI KOMEN / RESPONS KEPADA ARTIKEL DI ATAS, SILA PILIH "COMMENT AS" DI BAWAH SEBAGAI ANONYMOUS ATAU NAME / URL. TAIP NAMA & ABAIKAN URL. TQ

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