Tentukan himpunan penyelesaian dari persamaan kuadrat berikut. Soal: 1. 4x² – 5x = 0 2. x² – 9 = 0 3. x² + 2x – 3 = 0 4. 2x²+ 10x + 12 = 0 5. 6x²+ 13x – 5 = 0

Penjelasan dengan langkah-langkah:

1) 4x – 2x² = 0

2x(2 – x) = 0

2x = 0 —> x = 0

atau

2 – x = 0

2 = x

2)25 – x² = 0

(5 – x)(5 + x) = 0

5 = x atau -5 = x

3) x² – 8x = 0

x(x – 8) = 0

x = 0

atau

x – 8 = 0 —> x = 8

4) x² – x – 20 = 0

(x – 5)(x + 4) = 0

x – 5 = 0 —> x = 5

atau

x + 4 = 0 —> x = -4

5) 4x² – 1 = 0

(2x – 1)(2x + 1) = 0

2x – 1 = 0 —> 2x=1 –> x = ½

2x +1 = 0 –> 2x = -1 –> x=-½

6) 16p² – 36 = 0

(4p – 6)(4p + 6) = 0

4p= 6 —> p = 6/4

atau

4p=-6 —> p = – 6/4

7) x² – 8x – 9 = 0

(x + 1)(x – 9) = 0

x = -1 atau x = 9

8) 2x² + 6x – 8 = 0

(2x – 2)(x + 4) = 0

2x = 2 —> x = 1

atau

x = -4

9) -x² + 4x – 4 = 0

(-x + 2)(x – 2) = 0

-x = – 2 —> x = 2

atau

x = -2

10) 2x² + 6x – 20 = 0

(2x + 10)(x – 2) = 0

2x = -10 —> x = -5

atau

x = 2