If the quadratic equation ax2+2cx+b=0  and ax2 +2bx + c =0  (b≠c) have a common root then a + 4b + 4c is equal to

The given Quadratic equations are ax2+2cx+b=0  …… ( 1 ) ax2 +2bx + c =0 ….. ( 2 )Subtract Eq (2) from Eq (1) then we get ax2+2cx+b−(ax2 +2bx + c) = 0 then we get2x(c−b)+(b−c)=0⇒x=12 So 12 is a common root for both the equationsNow substitute x  value in Eq ( 1 )       (or take Eq ( 2 ))From Eq (1)⇒ a(12)2+ 2c(12)+ b= 0 ⇒a4+c+b=0 ∴ a+4b+4c=0