Results 1 to 11 of 11
Like Tree2Thanks
  • 1 Post By topsquark
  • 1 Post By SlipEternal

Math Help - Comparing coefficients in quadratic?

  1. #1
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Comparing coefficients in quadratic?

    Say I have 2 quadratics

    p(x^2)+qx=r=0 and d(x^2)+ex+f=0 with one common root

    can i write (p/d)=(q/e)=(r/f) ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,079
    Thanks
    375
    Awards
    1

    Re: Comparing coefficients in quadratic?

    Quote Originally Posted by AaPa View Post
    Say I have 2 quadratics

    p(x^2)+qx=r=0 and d(x^2)+ex+f=0 with one common root

    can i write (p/d)=(q/e)=(r/f) ?
    Can you?

    Compare: 2x^2 + x - 1 vs. 2x^2 + 3x - 2

    -Dan
    Thanks from AaPa
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Re: Comparing coefficients in quadratic?

    no.
    so when can we compare coefficients?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,931
    Thanks
    782

    Re: Comparing coefficients in quadratic?

    If p(x),q(x) are two polynomials with the exact same set of roots and the same degree, then p(x) = kq(x) where k is some constant. That is when you can compare coefficients.
    Thanks from AaPa
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Re: Comparing coefficients in quadratic?

    All my confusions which troubled me have disappeared. You really made me think on my own.

    Thank you very very muchh!!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Re: Comparing coefficients in quadratic?

    hey

    like comparing coefficients.

    can we compare exponents as in this given equation

    [(a^n) + (b^n)]/[(a^n-1) + (b^n-1)] = (a+b)/2
    (n-1 is exponent)

    to get n=1


    if yes then what is the condition that allows us to compare?
    Last edited by AaPa; November 1st 2013 at 02:26 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Re: Comparing coefficients in quadratic?

    [itex]a^n + b^n / a^n-1 +b^n-1 = a+b / 2[/itex]
    Last edited by AaPa; November 1st 2013 at 10:07 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    174
    Thanks
    85

    Re: Comparing coefficients in quadratic?

    Maybe this will help

    Two quadratic polynomials

    x^2 + b x + c

    x^2 + s x + t

    have a root in common if and only if

    c^2 - b c s + c s^2 + b^2 t - 2 c t - b s t + t^2 = 0
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Re: Comparing coefficients in quadratic?

     \frac {a^n + b^n} { a^{n-1} + b^{n-1}} = \frac{a+b} {2}

    by comparing exponents we get n=1
    exactly when can we compare exponents like this?
    Last edited by AaPa; November 2nd 2013 at 04:30 AM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,079
    Thanks
    375
    Awards
    1

    Re: Comparing coefficients in quadratic?

    Quote Originally Posted by AaPa View Post
     \frac {a^n + b^n} { a^{n-1} + b^{n-1}} = \frac{a+b} {2}

    by comparing exponents we get n=1
    exactly when can we compare exponents like this?
    Well...We can solve this in terms of a and b: b = -a for odd n, so there is no specific relationship needed for n. But generally we can match coefficients of terms on each side of an equation if the terms are members of an orthogonal series. The "power series" is such a series: a_0 + a_1x + a_2 x^2 + .... Many other orthogonal expansions exist but you'll see the power series the most often.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Mar 2012
    From
    India
    Posts
    85

    Re: Comparing coefficients in quadratic?

    let us say that a and b are positive distinct real natural numbers....is there any other value of n that satisfies the equation? how do we tell?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. General question about comparing coefficients
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 6th 2012, 11:38 AM
  2. Replies: 4
    Last Post: July 1st 2012, 04:01 AM
  3. Replies: 1
    Last Post: June 19th 2012, 06:25 AM
  4. Replies: 3
    Last Post: March 11th 2011, 07:27 PM
  5. comparing coefficients
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 14th 2009, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum