Results 1 to 4 of 4

Math Help - Finding value of a constant c in standard form of quadratic equation

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    131

    Finding value of a constant c in standard form of quadratic equation

    The equation is 16x^(2) -24x+c=0 What is c, given that one root is twice the other root?

    I made one root r and the other root 2r. I know the -b/a and the c/a relationships (-b/a is the sum of the roots and c/a is the product). Thanks for the help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1

    Re: Finding value of a constant c in standard form of quadratic equation

    Quote Originally Posted by benny92000 View Post
    The equation is 16x^(2) -24x+c=0 What is c, given that one root is twice the other root?
    The sum of the roots is \frac{24}{16}~.

    The product of the roots is \frac{c}{16}~.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: Finding value of a constant c in standard form of quadratic equation

    Let's just think about this for a moment. If there are two roots, a and b, what does it look like? Where did those relationships come from?

    (x-a)*(x-b) = x^2 - (a+b)x + ab

    This should suggest that the produce to the roots IS the constant term! Use this to your advantage.

    16x^2 - 24x + c = 16(x^2 - (3/2)x + (c/16))

    Using your notation, r * 2r = c/16 and you are almost done.

    Also, notice how the opposite of the coefficient on the linear term is the SUM of the roots!

    Using your notation, r + 2r = 3/2.

    Go ahead and build structures and explore the problem. There is just no need to KNOW how to proceed before you think you are solving the problem. Invent a solution!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2008
    Posts
    131

    Re: Finding value of a constant c in standard form of quadratic equation

    And how would we solve for the roots themselves?

    Edit: I posted this at the same time as you. Give me a second to read

    I came up with C=8 and the roots are 1/2 and 1.Touche..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding an equation in standard form
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 20th 2011, 06:10 PM
  2. Replies: 3
    Last Post: March 10th 2010, 08:33 AM
  3. Replies: 2
    Last Post: March 9th 2010, 08:33 PM
  4. Replies: 1
    Last Post: March 9th 2010, 08:48 AM
  5. Replies: 14
    Last Post: May 30th 2008, 06:10 AM

Search Tags


/mathhelpforum @mathhelpforum