Question

If the quadratic equations ax + 2bx + c = 0 and ax + 2cx + b = 0,(b + c) have a common root then show that a + 4b + 4c = 0.(full explanation)
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Answer 1

Answer:

Considering the equations to be

ax 2+2cx+b=0...(1)

ax 2+2bx+c=0...(2)

(2)-(1) gives

2(b−c)x+c−b=0

2(b−c)x=b−c

2x=1

∴x= 1/2

From (1)

ax 2+2cx+b=0

a( 1/2)^2+2c1/2+b=0

a+4c+4b=0