If the quadratic equation ax^2 + 2cx + b = 0 and ax^2 +2bx + c = 0, (b != c), have a common root then a + 4b + 4c is equal to?

A) -2
B) -1
C) 0
D) 1

1 Answer
Aug 19, 2017

Answer is (c)

Explanation:

As ax^2+2cx+b=0 and ax^2+2bx+c=0, where b!=c i.e. b-c!=0

subtracting first from second we get

2x(b-c)+c-b=0

or 2x(b-c)=b-c and dividing by b-c, we have x=1/2, which is the common root.

Further, as ax^2+2cx+b=0, for x=1/2 we have a/4+c+b=0 i.e. a+4c+4b=0.

Hence answer is (c)