If the quadratic equations, `a x^2+2c x+b=0 and a x^2+2b x+c=0(b!=c)` have a common root, then `a+4b+4c` is equal to: a. -2 b. 2 c. 0 d. 1

Options

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

Answer

C

Explanation

Let `alpha` be the common root of the given equations. Then, `a alpha^(2) + 2 c alpha + b = 0 and, a alpha^(2) + 2 b alpha + c = 0`
`2 alpha(c-b) + (b-c) = 0" "["On subtracting"]`
`alpha =(1)/(2)" "[because b ne c]`
Putting `alpha = 1//2 "in" a alpha^(2) + 2 c alpha + b = 0`, we get `a + 4b + 4c = 0`.