1.4.1 Punca Persamaan Kuadratik (Contoh Soalan)

Soalan 1:

Selesaikan persamaan kuadratik,

\frac{2 x^{2} - 5}{3} = 3 x

Penyelesaian:

\frac{2 x^{2} - 5}{3} = 3 x

2x²– 5 = 9x

2x²– 9x – 5 = 0

(x – 5) (2x + 1) = 0

x – 5 = 0 atau 2x + 1 = 0

x = 5, x = –½

Soalan 2:

Selesaikan persamaan kuadratik, 4x² – 12 = –13x.

Penyelesaian:

4x²– 12 = –13x

4x²+ 13x – 12 = 0

(4x – 3) (x + 4) = 0

4x – 3 = 0 atau x + 4 = 0

x = ¾, x= – 4

Soalan 3:

Selesaikan persamaan kuadratik, 5x² = 3(x + 2) – 4.

Penyelesaian:

5x²= 3(x + 2) – 4

5x²= 3x + 6 – 4

5x² – 3x – 2 = 0

(x – 1) (5x + 2) = 0

x – 1 = 0 atau 5x + 2 = 0

x = 1,

x = - \frac{2}{5}

Soalan 4:

Selesaikan persamaan kuadratik,

\frac{3 x (x - 3)}{4} = - x + 3.

Penyelesaian:

\frac{3 x (x - 3)}{4} = - x + 3

3x²– 9x = –4x + 12

3x² – 5x – 12 = 0

(x – 3) (3x + 4) = 0

x – 3 = 0 atau 3x + 4 = 0

x = 3,

x = - \frac{4}{3}