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Tabbiejack Group Title

What is the value of c such that: x2 + 14x + c, is a perfect-square trinomial?<o:p></o:p> A. 7 B. 98 C. 196 D. 49

  • one year ago
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  1. passive13 Group Title
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    D

    • one year ago
  2. Jhannybean Group Title
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    \[x^2+14x+c=0\]

    • one year ago
  3. ParthKohli Group Title
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    Observe that a perfect square is in the form \((a + b)^2 = a^2 + 2ab + b^2\). The first term is \(x^2 \) so we get an idea that the perfect square is in the form \((x + b)^2\). Now the middle term is \(2ab\) and here it is \(14x\). We know that \(a = x\) and so \(2x b = 14x \Rightarrow b = 7\). And so we have \((x + 7)^2 = x^2 + 14x + 49\). There's another technique which you can use formally, which is called "Completing the Square". It's just a rip-off of what I did above.

    • one year ago
  4. ParthKohli Group Title
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    That technique says that you get the half of the coefficient of \(x\), and square it to get the last term. So you get the half of \(14\) which is \(7\). The square of that is \(49\).

    • one year ago
  5. Jhannybean Group Title
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    |dw:1369717242091:dw|

    • one year ago
  6. Tabbiejack Group Title
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    ok it is easier to see it like that

    • one year ago
  7. Tabbiejack Group Title
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    I have another question if you don't mind

    • one year ago
  8. Tabbiejack Group Title
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    Graph the set of points. Which model is most appropriate for the set? ( 1, 20), (0, 10), (1, 5), (2, 2.5)

    • one year ago
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