if for the two real constants a and b the expression a*x^3+3*x^2+8*x+b is exactly divisible by (x+2) and (x-2) then value of a and b ???

• Ans: a=-2 & b=-12
  
  Substituting the value of x=2 and x=-2 in the given equation leads us to following two equation having solution(other equation obtained has no solution)
  8a+b=-28 & 8a-b=-4
  Solving these two equations, we get,
  a=-2 and b=-12
• 13 years agoHelpfull: Yes(11) No(6)
• a*x^3+3*x^2+8*x+b this equation have three roots,
  let roots are -2, 2 and p
  sum of product of two roots at a time = 8/a
  => -2*2+2*p-2*p=8/a
  => -4= 8/a
  => a= -2
  replace x---> 1/x, the equation becomes b*x^3+8*x^2+3*x+a have roots 1/2, -1/2 and 1/p,
  sum of product of two roots at a time = 3/b
  => (1/2)(-1/2)+(1/2)(1/p)+(-1/2)(1/p) = 3/b
  => -1/4= 3/b
  => b = -12
• 12 years agoHelpfull: Yes(9) No(5)
• Ans. a= -2, b= -12
  (x+2)(x-2)(-2x+3)= (x^2-4)(-2x+3)= -2x^3+8*x+3x^2-12, giving a= -2, b= -12
  
• 13 years agoHelpfull: Yes(5) No(4)