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34kurt
3 years ago
11

I need help on the Quadratic Formula.

Mathematics
1 answer:
sasho [114]3 years ago
4 0
1. 3x² + 12x - 15 = 0
    x = <u>-(12) +/- √((12)² - 4(3)(-15))</u>
                             2(3)
    x = <u>-12 +/- √(144 + 180)</u>
                           6
    x = <u>-12 +/- √(324)
</u>                     6<u>
</u>    x = <u>-12 +/- 18 </u>
                  6
    x = -2 <u>+</u> 3
    x = -2 + 3                 x = -2 - 3
    x = 1                         x = -5
--------------------------------------------------------------------------------------------
2. 5x² + 11x + 2 = 0
    x = <u>-(11) +/- √((11)² - 4(5)(2))</u>
                           2(5)
    x = <u>-11 +/- √(121 - 40)</u>
                       10
    x = <u>-11 +/- √(81)
</u>                  10
    x = <u>-11 +/- 9</u>
                10
    x = -1¹/₁₀ <u>+</u> ⁹/₁₀
    x = -1¹/₁₀ + ⁹/₁₀        x = -1¹/₁₀ - ⁹/₁₀
    x = ¹/₅                      x = -2
--------------------------------------------------------------------------------------------
3. 2x² - 11x + 14 = 0
    x = <u>-(-11) +/- √((-11)² - 4(2)(14))</u>
                             2(3)
    x = <u>11 +/- √(121 - 102)</u>
                         6
    x = <u>11 +/- √(9)</u>
                  6
    x = <u>11 +/- 3</u>
                6
    x = 1⁵/₆ <u>+</u> ¹/₂
    x = 1⁵/₆ + ¹/₂          x = 1⁵/₆ - ¹/₂
    x = 2¹/₃                  x = 1¹/₃
--------------------------------------------------------------------------------------------
4. 2x² - x - 15 = 0
    x = <u>-(-1) +/- √((-1)² - 4(2)(-15))</u>
                            2(2)
    x = <u>1 +/- √(1 + 120)</u>
                      4
    x = <u>1 +/- √(121)</u>
                   4
    x = <u>1 +/- 11</u>
                4
    x = ¹/₄ <u>+</u> 2³/₄
    x = ¹/₄ + 2³/₄          x = ¹/₄ - 2³/₄
    x = 3                      x = 2¹/₂
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