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Thread: Algebra II: Complex Numbers & Trinomials & Factoring

  1. #1
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    Algebra II: Complex Numbers & Trinomials & Factoring

    I need help with these problems please:
    Solve by Factoring:
    $\displaystyle 3x^2 + 6x - 24 = 0$
    The problem i got is that any combination of number I got that produced -24 didn't add to 6.

    And:

    $\displaystyle 5x^2 - 40x - 45 = 0$

    And:

    $\displaystyle 9x^2 + 24x + 16$

    Solve the equation.
    $\displaystyle 4x^2 + 9 = 0$
    The answers were:
    a. $\displaystyle \frac{-3}{2}i, \frac{3}{2}i $ b. $\displaystyle \frac{-9}{4}i , \frac{9}{4}i$

    Use the Quadratic Formula to solve the equation.
    $\displaystyle -2x^2 - 5x + 3 = 0$
    My solution didn't match the 2 possible answers provided:
    $\displaystyle \frac{-27}{2} , 11 $ and $\displaystyle -3 , \frac{1}{2} $

    $\displaystyle 4x^2 - x + 9 = 0$
    provided possible answers:
    $\displaystyle \frac{1}{4} +- \frac{i\sqrt143}{4}$ or $\displaystyle \frac{1}{8} +- \frac{i\sqrt143}{8}$

    I know its kind of alot but I absolutely cannot figure this out! Help is very appreciated
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  2. #2
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    Quote Originally Posted by Drew_445 View Post
    I need help with these problems please:
    Solve by Factoring:
    $\displaystyle 3x^2 + 6x - 24 = 0$
    The problem i got is that any combination of number I got that produced -24 didn't add to 6.

    Mr F says: Start by writing it as 3(x^2 + 2x - 8) = 0.

    And:

    $\displaystyle 5x^2 - 40x - 45 = 0$

    Mr F says: Start by writing it as 5(x^2 - 8x - 9) = 0.

    And:

    $\displaystyle 9x^2 + 24x + 16$

    Mr F says: This has the form of a perfect square.

    Solve the equation.
    $\displaystyle 4x^2 + 9 = 0$

    Mr F says: $\displaystyle {\color{red}x^2 = -\frac{9}{4} \Rightarrow x = \sqrt{-\frac{9}{4}} = \pm i \, \frac{3}{2}}$.

    The answers were:
    a. $\displaystyle \frac{-3}{2}i, \frac{3}{2}i $ b. $\displaystyle \frac{-9}{4}i , \frac{9}{4}i$

    Use the Quadratic Formula to solve the equation.
    $\displaystyle -2x^2 - 5x + 3 = 0$
    My solution didn't match the 2 possible answers provided:
    $\displaystyle \frac{-27}{2} , 11 $ and $\displaystyle -3 , \frac{1}{2} $

    Mr F says: Show your working.

    $\displaystyle 4x^2 - x + 9 = 0$
    provided possible answers:
    $\displaystyle \frac{1}{4} +- \frac{i\sqrt143}{4}$ or $\displaystyle \frac{1}{8} +- \frac{i\sqrt143}{8}$

    Mr F says: Show your working.

    I know its kind of alot but I absolutely cannot figure this out! Help is very appreciated
    ..
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  3. #3
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    Use the Quadratic Formula to solve the equation.


    Mr F says: Show your working.

    $\displaystyle x = \frac{5 +- \sqrt25-4(-2)(3)}{-4}$

    $\displaystyle \frac{5 +- \sqrt1}{-4}$
    So the solution I got was +-5 over 4, which doesn't answer any of the possible answers.

    So what do i do?
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  4. #4
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    Quote Originally Posted by Drew_445 View Post
    Use the Quadratic Formula to solve the equation.


    Mr F says: Show your working.

    $\displaystyle x = \frac{5 +- \sqrt25-4(-2)(3)}{-4}$ Mr F says: Correct.

    $\displaystyle \frac{5 +- \sqrt1}{-4}$ Mr F says: Wrong.

    So the solution I got was +-5 over 4, which doesn't answer any of the possible answers.

    So what do i do?
    $\displaystyle x = \frac{5 \pm \sqrt{25 - 4(-2)(3)}}{-4} = \frac{5 \pm \sqrt{25 {\color{red}+} 24}}{-4} = \frac{5 \pm 7}{-4} = -3, ~ \frac{3}{4}$.
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  5. #5
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    oh wow such a simple solution

    thanks very much
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