Let f(x) = ax2 + bx + c, where a,b and c are certain constants and a#0. It is known that f(5) = -3f(2) and that 3 is a root of f(x) = 0. What is the other root of f(x) = 0

a. -7

b. -4

c. 2

d. 6

• b. -4
  f(5) = -3f(2)
  => f(5)+ 3f(2)= 0
  => 25a + 5b + c + 3(4a +2b + c) = 0
  => 37a + 11b + 4c = 0 -------(1)
  
  given, f(3)=0
  => 9a + 3b + c = 0
  => 36a + 12b + 4c = 0 --------(2)
  
  (1)-(2) gives a = b
  
  so, eqn is ax^2 + ax + c = 0
  
  sum of roots = (3+k)= -a/a = -1 where, k is other root
  => k = -4
• 10 years agoHelpfull: Yes(7) No(0)
• since 3 is a root of f(x) then the equation becomes 9a+3b+c=0(1)
  Also f(5)=-3f(2) therefore 25a+5b+c=-3(4a+2b+c) it equals to 37a+11b+4c=0(2)
  on solving (1)&(2) we get a-b=0;a=b.
  3+other root is -1
  so answer is option (b).
• 10 years agoHelpfull: Yes(0) No(0)