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Math Help - Need an example fill out please :)

  1. #1
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    Need an example fill out please :)

    Hello
    The math problems im gonna post below may be below most of you but i missed a few days of shcool so i didn't lear how to solve these equations. the teacher let me copy down what they were but she didn't have time to teach me them before the hilidays so i was hoping someone could kinda explain what they are doing when solving them correctly. This would be a big help as i do have to write a test on equations like these in the new year.
    Thanks

    Communication Equatuions:

    Example 1:
    Write a quadratic equation whose roots are -2 and 3. is it possible to write more then one equation? Explain

    Example 2:
    Can x(x-3)=0 be solved by dividing both sides of the equation by x? explain

    Example 3:
    If the product of two factors is zero, what must be true of the factors.
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  2. #2
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    Quote Originally Posted by Dakkar View Post
    Example 1:
    Write a quadratic equation whose roots are -2 and 3. is it possible to write more then one equation? Explain
    This works, but why..? A question for you to answer:

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

    Multiplying it out to standard form:

    x^2 - x - 6 = 0

    Looking at the above, is this the only possible answer?
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  3. #3
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    Quote Originally Posted by Dakkar View Post
    Example 2:
    Can x(x-3)=0 be solved by dividing both sides of the equation by x? explain
    If I did divide both sides by x, I'd get

    x - 3 = 0

    Hmm. Now we're saying this quadratic equation only has one root, +3. Possibly something unfortunate has happened to the other root along the way ...
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  4. #4
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    Quote Originally Posted by Dakkar View Post
    Example 3:
    If the product of two factors is zero, what must be true of the factors.
    Can't answer this one until I know what you mean by factors. Factors of a number? Factors of an equation?
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  5. #5
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    (x+2)(x-3)=0 is correct because when placed in brackets -2 and 3 become there opposites so -2 becomes 2 and 3 becomes -3?

    x2-x-6=0 is the only possible way to write it because if change -6 to +6 u would be unable to factor this equation?

    Not sure how close this is to being correct
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  6. #6
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    Oh I think it is factors of an equation for example 3
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  7. #7
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    Quote Originally Posted by Dakkar View Post
    (x+2)(x-3)=0 is correct because when placed in brackets -2 and 3 become there opposites so -2 becomes 2 and 3 becomes -3?
    That's one way of looking at it, but there's a better one. The (x + 2) term is there because when you substitute in x = -2, the entire term becomes zero, regardless of the value of the other term. Same for (x - 3): when x = 3, the entire equation is zero ... the other term doesn't even get a vote.

    Quote Originally Posted by Dakkar View Post
    x2-x-6=0 is the only possible way to write it because if change -6 to +6 u would be unable to factor this equation?
    Well ...

    If I wrote (x + 2)(x - 3) = 0, what if I multiplied by some random constant all the way across the equation? Say we decided to multiply by 5 for no good reason. Then 5(x + 2)(x - 3) = 5(0), or 5x^2 - 5x - 30 = 0. This still works for the roots x = -2 or x = 3, as you can verify.
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  8. #8
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    Quote Originally Posted by Dakkar View Post
    Example 3:
    If the product of two factors is zero, what must be true of the factors.
    Quote Originally Posted by Dakkar View Post
    Oh I think it is factors of an equation for example 3
    Then I could rephrase this as:

    If (x + a) and (x + b) are two factors for some unknown quadratic, and (x + a)(x + b) = 0, then what must be true of the factors?
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  9. #9
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    Either one of the factors must be 0...
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