Algebra help.....?

Please help me !

Thanks !

Attachment image

1 Answer

Relevance
  • 6 months ago
    Favorite Answer

    Given q^2-4pr>0 & p>0.

    f(x)=log[px^3+(p+q)x^2+(q+r)x+r]

    =>

    f(x)=log[(x+1)(px^2+qx+r)]

    =>

    f(x)=log{p(x+1)[(x+q/(2p))^2-

    [sqr(q^2-4pr)/(2p)]^2]}

    (completing the square)

    =>

    f(x)=log{p(x+1)[(x+q/(2p))^2-

    [sqr(D)/(2p)]^2]}

    (where D=q^2-4pr)

    =>

    Dom(f(x))

    =

    (x>-1) & [{(x+q/(2p))^2-[sqr(D)/(2p)]^2}>0]

    =

    (x>-1) & [(x<-(sqr(D)+q)/(2p)) or (x>(sqr(D)-q)/(2p)]

    =

    (x>-1) & (x<-(sqr(D)+q)/(2p)

    or

    (x>-1) & (x>(sqr(D)-q)/(2p)

    • ...Show all comments
    • JOHN
      Lv 7
      6 months agoReport

      Well done, Pinkgreen. I attemptred this, got the factorisation, but got tangled up in the inequalities and abandoned the problem.

    • Login to reply the answers
Still have questions? Get your answers by asking now.