quadratic equation.

methods of solving a quadratic equation:

(1) By factorization

(2) By completing the square

(3) By quadratic formula

(4) By graphical method

圖片參考:http://imgcld.yimg.com/8/n/HA00101881/o/2013092120...

1 個解答

評分
  • 6 年 前
    最佳解答

    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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