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A maths - Quadratic equation and inequalities

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  • bonkysleuth
    bonkysleuth's Avatar
    188 posts since Mar '07
    • 06 May `08, 7:09PM

      find the value of a and of b for which,

      (a) x^2 + ax < b is only satisfied by -2 < x <4 

       

      (b) 2x^2 + a > bx is only satisfied by x < -2 or x>3

       

      Answers (a) a= -2 , b= 8   (b) a=-12 , b = 2

       

      please lend me a hand in solving this. having an exam tomorrow, so please do state the workings clearly. thanks!

  • Moderator
    eagle
    eagle's Avatar
    14,472 posts since Aug '01
    • 06 May `08, 7:18PM

      me also have exam tmr, but well

      a) x^2 + ax - b < 0
      smiling curve smaller than 0, so roots at -2 and 4
      so x^2 + ax - b = (x+2)(x-4) = x^2 -2x -8

      hence a = -2,
      -b = -8 => b=8

       

      b) 2x^2 - bx + a > 0 or x^2 - b/2 x + a/2 > 0
      smiling curve again, and roots at x=-2 and x=3
      so x^2 - b/2 x + a/2 = (x+2)(x-3) = x^2 - 5x -6
      a/2 = -6 => a = -12
      -b/2 = -5 => b = 10

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