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Math Help - perfect square of trinomials

  1. #1
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    perfect square of trinomials

    The question is:
    Which of the following polynomials is NOT a perfect square trinomial?
    A) x2 + 2x + 1
    B) 4x2 - 4x + 1
    C) x2 + 3x + 9
    D) 16x2 + 8x + 1
    E) all of them are perfect square trinomials

    the way it is explained in my lesson is very confusing. I am very confused. please help me!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by starrynight View Post
    The question is:
    Which of the following polynomials is NOT a perfect square trinomial?
    A) x2 + 2x + 1
    B) 4x2 - 4x + 1
    C) x2 + 3x + 9
    D) 16x2 + 8x + 1
    E) all of them are perfect square trinomials

    the way it is explained in my lesson is very confusing. I am very confused. please help me!
    Look at the quadratic formula for a moment:
    x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    Now, if the discriminant (the b^2 - 4ac) is equal to 0 then then you are adding \pm 0 to the -b in the numerator. Thus the two roots of the quadratic will be the same, ie. the quadratic is a perfect square.

    So for which of these is the discriminant equal to 0?

    -Dan
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  3. #3
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    I think the answer is x2 + 3x + 9. Am I right?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by starrynight View Post
    I think the answer is x2 + 3x + 9. Am I right?
    Well, as the rest give a discriminant of 0 and this one has a discriminant of 9 - 4 \cdot 9 = -27 \neq 0, I'd say "yes."

    -Dan
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