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Math Help - equations and quadratic functions

  1. #1
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    equations and quadratic functions

    Please help, I'm really confused.

    1) If x + mx + n is a perfect square, show that m=4n

    and

    2) find value of k

    x + (2k+10)x + k + 5 = 0

    Help would be much appreciated. Thanks.
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  2. #2
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    Hello, lra11!

    1) If x^2 + mx + n is a perfect square, show that: . m^2 = 4n

    If x^2+mx+n is a square, the equation x^2 + mx + n \:=\:0 has one root.

    If a quadratic equation has one root, its discriminant (b^2-4ac) is zero.

    Hence: . m^2 - 4n \:=\:0

    Therefore: . m^2\:=\:4n



    2) Find value of k

    . . x^2 + (2k+10)x + k^2 + 5 \:= \:0

    What are the conditions for this quadratic equation?

    As given, k can be any number  \geq -2.

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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lra11 View Post
    Please help, I'm really confused.

    1) If x + mx + n is a perfect square, show that m=4n
    remember what you do when you are completing the square? if a quadratic is a complete square, it means that the constant is the square of 1/2 of the coefficient of x. thus, if x^2 + mx + n is a complete square, it follows immediately that n = \left( \frac m2 \right)^2 and the rest is trivial
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  4. #4
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    question 2

    the equation has equal roots
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lra11 View Post
    the equation has equal roots
    then the discriminant must be exactly zero, so you can still use what Soroban did, but without the inequality this time
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