Question

Find the condition for the equations ax2 + bx + c = 0 and a'x 2 + b'x + c' = 0 to have
reciprocal roots.​

Answer 1

Answer:

The condition for the equations ax2+bx+c=0 and a′x2+b′x+c′=0 to have reciprocal roots is c′a=b′b=a′c.

Answer 2

Answer:

Given ax

2

+bx+c=0 ....(1)

and a

1

x

2

+b

1

x+c

1

=0 ....(2)

Replacing x by

x

1

in (2) we get

c

1

x

2

+b

1

x+a

1

=0 ....(3)

Let α be a common root of (1) and (3)

Solving (1) and (3), we get

α=

ab

1

−bc

1

cc

1

−aa

1

=

cc

1

−aa

1

ba

1

−b

1

c

⇒(cc

1

−aa

1

)

2

=(ab

1

−bc

1

)(ba

1

−b

1

c)

Hence, option 'C' is correct.