1.5.1 SPM Praktis (Soalan Panjang)

SPM Praktis (Soalan Panjang)

Soalan 1:

Selesaikan persamaan kuadratik, (y + 3)(y – 4) = 30

Penyelesaian:

(y + 3)(y – 4) = 30

y²– 4y + 3y – 12 = 30

y²– y – 12 – 30 = 0

y²– y – 42 = 0

(y + 6)(y – 7) = 0

y + 6 = 0, y = –6

y – 7 = 0

y = 7

Soalan 2:

Selesaikan persamaan kuadratik, 5x² = 3( x – 2) + 8

Penyelesaian:

5x²= 3( x – 2) + 8

5x²= 3x – 6 + 8

5x²– 3x – 2 = 0

(5x + 2)(x – 1) = 0

5x + 2 = 0, x =

- \frac{2}{5}

Atau

x – 1 = 0

x = 1

Soalan 3:

Selesaikan persamaan kuadratik,

\frac{2 p^{2} - 15}{p} = 7

Penyelesaian:

\frac{2 p^{2} - 15}{p} = 7

2p²– 15 = 7p

2p²–7p – 15 = 0

(2p + 3)(p – 5) = 0

2p + 3 = 0, p =

- \frac{3}{2}

p – 5 = 0

p = 5

Soalan 4:

Selesaikan persamaan kuadratik,

y (y - \frac{9}{2}) = \frac{5}{2}

Penyelesaian:

\begin{array}{l} y (y - \frac{9}{2}) = \frac{5}{2} \\ y^{2} - \frac{9 y}{2} = \frac{5}{2} \end{array}

(×2), 2y²– 9y = 5

2y²– 9y – 5 = 0

(2y + 1)(y – 5) = 0

2y + 1 = 0, y = ½

Atau

y – 5 = 0

y = 5