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Math Help - Quadratic Equation

  1. #1
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    Quadratic Equation

    Hi
    Can anyone plz. point out is there anything wrong with the question given below ?
    if its correct thrn how the solution will have to derived ?

    Question
    If α and β are the roots of the equation ax + bx + c = 0 then Prove that
    a 3b 2ab + 16ac = 0
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  2. #2
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    Quote Originally Posted by maskov View Post
    Hi
    Can anyone plz. point out is there anything wrong with the question given below ?
    if its correct thrn how the solution will have to derived ?

    Question
    If α and β are the roots of the equation ax + bx + c = 0 then Prove that
    a 3b 2ab + 16ac = 0
    Dear maskov,

    You should know that,

    \alpha+\beta=-\dfrac{b}{a}

    \alpha\beta=\dfrac{c}{a}

    Also, a^{2}- 3b^{2} - 2ab +16ac = 0

    \Rightarrow 1-3\left(\dfrac{b}{a}\right)^2-2\dfrac{b}{a}+16\dfrac{c}{a}=0

    Substitute for \dfrac{b}{a} ~and~\dfrac{c}{a} and see whether the left and right hand sides are equal.
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  3. #3
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    Hi
    Sudharaka
    Thanks for your reply, substituting values of α + β and αβ does not make it zero.

    Maskov
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  4. #4
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    Quote Originally Posted by maskov View Post
    Hi
    Can anyone plz. point out is there anything wrong with the question given below ?
    if its correct thrn how the solution will have to derived ?

    Question
    If α and β are the roots of the equation ax + bx + c = 0 then Prove that
    a – 3b – 2ab + 16ac = 0
    Do you have some condition relating the roots to each other ?
    Numerous combinations of a, b, c will not satisfy the 2nd equation,
    hence the roots ought to have a certain relationship.
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