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.

2. What is the other root of f(x) = 0?

• other root is -4
  since 3 is a root and let y be the other root
  (x-3)(x-y)=0
  f(5)=2*(5-y)
  f(2)=-1*(2-y)
  f(5)=-3*f(2)
  2*(5-y)=3*(2-y)
  y=-4
  
• 10 years agoHelpfull: Yes(18) No(4)
• A/C TO QUESTION
  F(X)=0,AND 3 IS THE ROOT OF F(X)=0
  THEN 9A+3b+C=0 .............. EQUATION FIRST
  ALSO IT IS GIVEN THAT F(5)=-3F(2)
  BY THIS EQUATION WE CAN GET THE EQUATION LIKE 25A+5B+C= -12A-6B-3C
  IT WILL COME LIKE 37A=11B+4C=0 EQUATION SECOND
  FOR SOLVING THESE TWO EQUATION WE CAN USE BRAZ GUNANKHAND METHOD
  3 1 9 3 .................FROM EQUATION FIRST FROM B TO B COEFFICIENT VALUE
  11 4 37 11 .................FROM EQUATION TWO " " " " " "
  A/(3*4-11*1)= B/(1*37-4*9)= C/(9*11-37*3)
  BY THIS THEOREM A=1,B=1,C= -12
  PUT THESE VALUE IN F(X)=0
  THE EXACT EQUATION WILL COME LIKE...... X^2+X-12=0
  X^2+4X-3X-12=0
  X(X+4)-3(X+4)=0
  (X-3)(X+4)=0
  X=3,-4
  THEN OTHER ROOT MUST BE -4(NEGATIVE VALUE OF 4).....
  
• 9 years agoHelpfull: Yes(2) No(0)