f4.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 28

    (1) By factorization

    (2x-5)² = (x-3)(6x-15)

    (2x-5)² = 3(x-3)(2x-5)

    (2x-5)² - 3(x-3)(2x-5) = 0

    (2x-5)[(2x-5) - 3(x-3)] = 0

    (2x-5)(2x-5-3x+9) = 0

    (2x-5)(-x+4) = 0

    (2x-5)(x-4) = 0

    x = 5/2 or x = 4

    (2) By completing the square

    (2x-5)² = (x-3)(6x-15)

    4x²-20x+25=6x²-15x-18x+45

    4x²-20x+25=6x²-33x+45

    2x²-13x+20=0

    x²-6.5x+10=0

    x²-6.5x+3.25² = -10+3.25²

    (x-3.25)² = 0.5625

    x - 3.25 = ±0.75

    x = 3.25±0.75

    x = 2.5 or x = 4

    (3) By quadratic formula

    (2x-5)² = (x-3)(6x-15)

    4x²-20x+25=6x²-15x-18x+45

    4x²-20x+25=6x²-33x+45

    2x²-13x+20=0

    x = [-(-13)±√[(-13)²-4(2)(20)]]/[2*2]

    x = (13±3)/4

    x = 10/4 or 16/4

    x = 5/2 or 4

    Question 30

    (1) By factorization

    (4-x)² - 5(4-x) - 14 = 0

    [(4-x)+2][(4-x)-7] = 0

    (6-x)(-3-x) = 0

    (x-6)(x+3) = 0

    x = 6 or x = -3

    (2) By completing the square

    (4-x)² - 5(4-x) - 14 = 0

    16-8x+x²-20+5x-14 = 0

    x²-3x-18 = 0

    x²-3x = 18

    x²-3x+1.5² = 18+1.5²

    (x-1.5)² = 20.25

    x-1.5 = ±4.5

    x = 1.5±4.5

    x = 6 or -3

    (3) By quadratic formula

    (4-x)² - 5(4-x) - 14 = 0

    16-8x+x²-20+5x-14 = 0

    x²-3x-18 = 0

    x = {-(-3)±√[(-3)²-4(1)(-18)] }/(2*1)

    x = {3±9}/2

    x = 12/2 or -6/2

    x = 6 or -3

    Question 32

    (1) By factorization

    (x+2)² - 81x² = 0

    (x+2)² - (9x)² = 0

    (x+2+9x)(x+2-9x) = 0

    (10x+2)(-8x+2) = 0

    (5x+1)(4x-1) = 0

    x = -1/5 or x = 1/4

    (2) By completing the square

    (x+2)² - 81x² = 0

    x² + 4x + 4 - 81x² = 0

    80x² - 4x - 4 = 0

    20x² - x - 1 = 0

    x² - x/20 - 1/20 = 0

    x² - x/20 + (1/40)² = 1/20 + (1/40)²

    (x - 1/40)² = 81/1600

    x - 1/40 = ±9/40

    x = 1/40 ± 9/40

    x = 10/40 or -8/40

    x = 1/4 or -1/5

    (3) By quadratic formula

    (x+2)² - 81x² = 0

    x² + 4x + 4 - 81x² = 0

    80x² - 4x - 4 = 0

    20x² - x - 1 = 0

    x = [-(-1)±√[(-1)²-4(20)(-1)]]/[2*20]

    x = (1±9)/40

    x = -8/40 or 10/40

    x = -1/5 or 1/4

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