herme519 發問於 科學及數學數學 · 7 年前

methods of solving a quadratic equation:

(1) By factorization

(2) By completing the square

(3) By quadratic formula

(4) By graphical method

### 1 個解答

• 7 年前
最愛解答

我只做 (1), (2), (3)。

(4)要畫圖再看相交點。

Question 24

(1) By factorization

3m² + 25/3 = 10m

9m² + 25 = 30m

9m² - 30m + 25 = 0

(3m - 5)² = 0

m = 5/3 (repeated)

(2) By completing the square

3m² + 25/3 = 10m

9m² + 25 = 30m

9m² - 30m + 25 = 0

(3m - 5)² = 0

m = 5/3 (repeated)

(3) By quadratic formula

3m² + 25/3 = 10m

9m² + 25 = 30m

9m² - 30m + 25 = 0

m = [-(-30)±√[(-30)²-4(9)(25)]]/[2*9]

m = (30±0)/18 = 5/3

Question 26

(1) By factorization

(a-2)(a+2) = (15/2) a

a² - 4 = (15/2) a

2a² - 8 = 15a

2a² -15a - 8 = 0

(2a+1)(a-8) = 0

a = -1/2 or a = 8

(2) By completing the square

(a-2)(a+2) = (15/2) a

a² - 4 = (15/2) a

2a² - 8 = 15a

2a² -15a - 8 = 0

a² -7.5a - 4 = 0

a² -7.5a = 4

a² -7.5a + (7.5/2)² = 4+ (7.5/2)²

(a - 3.75)² = 18.0625

a - 3.75 = ±4.25

a = 3.75±4.25

a = -0.5 or a = 8

(3) By quadratic formula

(a-2)(a+2) = (15/2) a

a² - 4 = (15/2) a

2a² - 8 = 15a

2a² -15a - 8 = 0

a = {-(-15)±√[(-15)²-4(2)(-8)] }/(2*2)

a = {15±√[225+64] }/4

a = {15±17}/4

a = -2/4 or 32/4

a = -1/2 or a = 8

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