Database - Quadratic Equation (Alpha and Beta)

• Ahm97sic

  17 Oct 08, 00:58

  Question 1

  Given that a and b are the roots of the equation x^2 = x - 2,

  show that a^4 = 2 - 3a

  Answer

  Step 1 : Subst x = a into the equation

  Since a is the root of the equation ie x = a, so we can substitute x = a into the

  equation ie

   x^2 = x - 2

  a^2 = a - 2            

  Step 2 : To do the proofing ie use the LHS to prove until it is equal to the RHS or use the RHS to prove until it is equal to the LHS

  LHS = a^4

         = (a^2)^2

         = (a-2)^2                         since a^2 = a - 2 

         = a^2 -4a + 4

         = a - 2 - 4a + 4                since a^2 = a - 2 

         = 2 - 3a

        = RHS (Shown)

  Now, you know the tricks that the "O" level  examiners used to set questions on this 4th pattern of the quadratic equation (alpha and beta) ie first substitute x = a into the equation, next use this result or some re-arranging of the result in the proofing.