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Math Help - roots of quadratic equation

  1. #1
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    roots of quadratic equation

    Mary saw this notation:

    3x^2 - 25x + 66 = 0 --> x1=4, x2=9

    Mary thought it seemed to be incorrect.

    She the realised that a number system other than decimal was used to determine the roots of the quadratic equation. What is the base of that number system (with an explantion pls)?
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  2. #2
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    Hello, the undertaker!

    Mary saw this notation: . 3x^2 - 25x + 66 = 0,\;\;x \:=\:4,9

    Mary thought it seemed to be incorrect.

    She then realised that a number system other than decimal was used.
    What is the base of that number system (with an explantion pls)?
    Let the base be b.

    Then 25 represents: . 2b+5
    and 66 represents: . 6b+6.

    Then the equation is: . 3x^2 - (2b+5)x + (6b+b) \:=\:0


    Since x = 4 is a root: . 3\cdot4^2 - (2b+5)\cdot4 + (6n+6) \:=\:0

    . . and we have: . 48 - 8b - 20 + 6b + 6 \:=\:0 \quad\Rightarrow\quad -2b \:=\:-34 \quad\Rightarrow\quad b \;=\:17


    The problem was written in base-seventeen.

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  3. #3
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    And, of course, using 9 instead of 4 gives exactly the same answer: b= 17.
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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, the undertaker!

    Let the base be b.

    Then 25 represents: . 2b+5
    and 66 represents: . 6b+6.

    Then the equation is: . 3x^2 - (2b+5)x + (6b+b) \:=\:0


    Since x = 4 is a root: . 3\cdot4^2 - (2b+5)\cdot4 + (6n+6) \:=\:0

    . . and we have: . 48 - 8b - 20 + 6b + 6 \:=\:0 \quad\Rightarrow\quad -2b \:=\:-34 \quad\Rightarrow\quad b \;=\:17


    The problem was written in base-seventeen.
    thanks a lot
    but wt does x2=9 have to do with the problem, because i dont think u included it
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