text: # Quadratic equation
  
  Printable View
  
  • Oct 19th 2008, 04:29 PM
  B-lap
  Quadratic equation
  The equation: x^3 - 3x^2 - 10x + 24 = 0
  
  has roots: 2, "h" and "k"
  
  Determine a quadratic equation whose roots are "h" - "k" and "hk"
  
  How do you do it?
  
  The anwser is: x^2 + 5x -84 = 0
  • Oct 19th 2008, 05:38 PM
  terr13
  I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
  (x-7)(x+12). Multiply it out to get the answer.
  
  (I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)