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Thread: Question on roots of a quadratic polynomial.

  1. #1
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    Question on roots of a quadratic polynomial.

    Check out the image . Question number 5


    Pls give me the solution...


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  2. #2
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    Re: Question on roots of a quadratic polynomial.

    Do you know the "quadratic formula"? What does the quadratic formula give for the two solutions to $\displaystyle x^2+ ax+ b= 0$? What is the difference between them? What does the quadratic formula give for the two solutions to $\displaystyle x^2+ bx+ a= 0$? What is the difference between them? Set those two differences equal. What does that give you?
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  3. #3
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    Re: Question on roots of a quadratic polynomial.

    Quote Originally Posted by HallsofIvy View Post
    Do you know the "quadratic formula"? What does the quadratic formula give for the two solutions to $\displaystyle x^2+ ax+ b= 0$? What is the difference between them? What does the quadratic formula give for the two solutions to $\displaystyle x^2+ bx+ a= 0$? What is the difference between them? Set those two differences equal. What does that give you?
    Sryi didnt get it



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    Re: Question on roots of a quadratic polynomial.

    Quote Originally Posted by sbjsavio View Post
    Check out the image . Question number 5


    Pls give me the solution...
    @sbjsavio. Please tell us why you post your images sideways?
    Do you expect us to stand on our heads?
    Do you really want help?
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  5. #5
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    Re: Question on roots of a quadratic polynomial.

    Quote Originally Posted by Plato View Post
    @sbjsavio. Please tell us why you post your images sideways?
    Do you expect us to stand on our heads?
    Do you really want help?
    Lol just a head exercise



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  6. #6
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    Re: Question on roots of a quadratic polynomial.

    Quote Originally Posted by sbjsavio View Post
    Lol just a head exercise
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    Well good luck $\sigma\mu\alpha\rho\tau~\alpha\sigma\sigma$.
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  7. #7
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    Re: Question on roots of a quadratic polynomial.

    Ok sorry for those silly things.
    Thank u guys i got it by solving.I used that quadratic formula method from hallofivy.
    Gud luck..


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  8. #8
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    Re: Question on roots of a quadratic polynomial.

    The roots of $\displaystyle x^2+ax+b=0$ are:

    $\displaystyle x=\frac{-a\pm\sqrt{a^2-4b}}{2}$

    Taking the difference $\displaystyle \Delta r_1$ to be the larger root minus the smaller, we have:

    $\displaystyle \Delta r_1=\sqrt{a^2-4b}$

    Likewise, for the second quadratic we would find:

    $\displaystyle \Delta r_2=\sqrt{b^2-4a}$

    If these differences are the same, this implies:

    $\displaystyle a^2-4b=b^2-4a$

    Can you proceed?
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  9. #9
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    Re: Question on roots of a quadratic polynomial.

    Quote Originally Posted by MarkFL View Post
    The roots of $\displaystyle x^2+ax+b=0$ are:

    $\displaystyle x=\frac{-a\pm\sqrt{a^2-4b}}{2}$

    Taking the difference $\displaystyle \Delta r_1$ to be the larger root minus the smaller, we have:

    $\displaystyle \Delta r_1=\sqrt{a^2-4b}$

    Likewise, for the second quadratic we would find:

    $\displaystyle \Delta r_2=\sqrt{b^2-4a}$

    If these differences are the same, this implies:

    $\displaystyle a^2-4b=b^2-4a$

    Can you proceed?
    I got the answer as a + b equals -4 and that is the correct answer given in my text books answer key. @MarkFL thank u brother


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