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?

Question

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

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Answer 1 · 2017-08-19T13:45:25

Answer is #(c)#

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)#