Maths-
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Question

If the quadratic equation a x squared plus 2 c x plus b equals 0 and a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis have a common root then a plus 4 b plus 4 c is equal to

  1. -2
  2. -1
  3. 0
  4. 1

Hint:

In the question the two equations have common root so we can let the root to be any variable then we will put the value of x in both the equations and subtract the equations then we will get the value of root after that we can put the value of root in the equation and get the required result.

The correct answer is: 0


    The two quadratic equations are a x squared plus 2 c x plus b equals 0 and a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis
    Let alpha be the common root.
    Now, a x squared plus 2 c x plus b equals 0 rightwards double arrow a alpha squared plus 2 c alpha plus b equals 0 _ _ _ _ _ _ _ _ _ _ _ _ e q u a t i o n space 1
    a x squared plus 2 b x plus c equals 0 rightwards double arrow a alpha squared plus 2 b alpha plus c equals 0 _ _ _ _ _ _ _ _ e q u a t i o n 2
    subtracting the equations, we get
    2 alpha left parenthesis c minus b right parenthesis plus left parenthesis b minus c right parenthesis equals 0
rightwards double arrow 2 alpha equals fraction numerator c minus b over denominator c minus b end fraction
rightwards double arrow alpha equals 1 half
    now putting the value in equation1
    a alpha squared plus 2 c alpha plus b equals 0
rightwards double arrow a open parentheses 1 half close parentheses squared plus 2 c 1 half plus b equals 0
rightwards double arrow a over 4 plus c plus b equals 0
rightwards double arrow a plus 4 b plus 4 c equals 0

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