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Math Help - Solving a Quadratic Equation by Modifying the Coefficient

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    Solving a Quadratic Equation by Modifying the Coefficient

    I'm working my way through Mathematics for the Nonmathematician and in the section on quadratic equations the author introduces a method of solving them that involves creating a new equation where the roots are the rots of the old one, each increased by one-half the coefficient of x. One of the exercise equations is:

    2x^2+8x+6=0

    but I don't know how to solve this due to the coefficient of x^2. Can anybody explain it to me?

    EDIT: It's actually the pq formula that's used.
    Last edited by drguildo; October 27th 2012 at 05:43 AM.
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    Hello!
    do uk quadratic formula or pq formula? any of them?
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    Quote Originally Posted by Petrus View Post
    Hello!
    do uk quadratic formula or pq formula? any of them?
    Do I know them? This book covers the pq formula (I think it's the same you're referring to). Actually I think I got my original post wrong and that's what is used to solve that quadratic. Either way I still can't figure out how to do it.
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    is factoring of the expression an accepted method? or do you refer to the factoring method as the pq method?
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    Quote Originally Posted by MAX09 View Post
    is factoring of the expression an accepted method? or do you refer to the factoring method as the pq method?
    The book says to solve it using the formula:

    \sqrt{{p^2 \over 4} - q} - {p \over 2}
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    i guess i am unfamiliar with this one... have no idea what p and q are.. good luck solving this one...
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    Hi!
    we know the pq formula goosh idk how to copy this but i give u the link Resultat av Googles bildsökning efter http://img97.imageshack.us/img97/1020/namnls5zf.jpg

    first we divide by 2 because x^2 need to be 1 in pq formula! so we got x^2+4x+3=0
    now if we use pq formula
    x1,2=-4/2+-sqrt((4/2)^2-3)
    can u finish this im sorry i cant use latex code so its alot easy to see what i do :S
    Thanks from drguildo
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    Thanks. I should have realised you can just divide the whole expression by 2. Oh well.
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    do u want me to solve this for u? or did u solve it by ur self?
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    2x^2 + 8x + 6 = x^2 + 4x + 3 = 0

    x = \sqrt{{4^2 \over 4} - 3} - {4 \over 2}

    x = \sqrt{4 - 3} - 2

    x = \sqrt{1} - 2

    x = 1 - 2

    x = -1

    and

    x = -\sqrt{{4^2 \over 4} - 3} - {4 \over 2}

    x = -\sqrt{4 - 3} - 2

    x = -\sqrt{1} - 2

    x = -1 - 2

    x = -3

    So x = 1 or x = -3
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    You are, I hope, aware that this is simply the quadratic formula?

    -Dan
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    I'm aware that there is a quadratic formula but not that it's equivalent to this.
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    U got some wrong it should be (-4/2) (ik that it dont really mather but a strange teacher can give u less point for that misstake
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    You are given to solve:

    2x^2+8x+6=0

    I would divide through by 2:

    x^2+4x+3=0

    I think the author wants you to then write:

    (x-2)^2+4(x-2)+3=0

    This equation will have two roots which are both 2 more than the original equation.

    (x^2-4x+4)+4(x-2)+3=0

    x^2-4x+4+4x-8+3=0

    x^2=1

    x=\pm1

    Thus, the roots of the original equation will be:

    x=-2\pm1

    x=-3,\,-1
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    Re: Solving a Quadratic Equation by Modifying the Coefficient

    Tbh the pq formula is quadratic formula but more stricter because x^2 needs to be alone
    Last edited by Petrus; October 28th 2012 at 11:14 PM.
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