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Maths (Honours) questions(Algebra+differentiation)- Help! Urgent!

  • 24-10-2011 9:17pm
    #1
    cocopopsxx
    Registered Users Posts: 261 ✭✭


    I really can't solve these two questions so need help asap.

    q1) One root of ax^2 + bx + c =0 differs by 3 from the other root. Show that b^2 = 9a^2 + 4ac.

    q2) F(x)= ax^3 + bx^2 + cx + d where a,b,c,d are constants. It has turning points at X=x1 and X=x2 and a point of inflexion at X=x3. Show that x1 + x2 = 2x3.

    (The X=x1, X=x2, X=x3 thing is actually like the newton/raphson x1 but I don't know how to type it :P)

    Any help would be appreciated! xxx


Comments

  • #2
    luciemc
    Registered Users, Registered Users 2 Posts: 81 ✭✭luciemc


    Q1:
    -use -b formula to find the two roots in terms of a,b,c
    -subtract bigger root from smaller root and let equal 3
    ...simplify by doing a bit of squaring and this will give you your answer...

    Q2:
    -find first derivative and let equal 0 to find x1 and x2
    -add them to give -2b/3a
    -find second derivative and let equal zero to find x3
    -x3=-b/3a
    -this shows x1+x2=2x3

    does this make sense...? i COULD write it out and scan but scanner is in another room and im lazy :p


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