Question

a^2b^2(a-2b)(a+4b), answer it fast​

Answer 1

YOUR ANSWER IS HERE The roots of (a

2

+b

2

)x

2

−2b(a+c)x+(b

2

+c

2

)=0 are equal.

i.e. D=b

2

−4ac=0

⇒4b

2

(a+c)

2

=4(a

2

+b

2

)(b

2

+c

2

)

⇒b

2

(a

2

+c

2

+2ac)=a

2

b

2

+a

2

c

2

+b

4

+b

2

c

2

⇒b

2

a

2

+b

2

a

2

+2ab

2

c=a

2

b

2

+a

2

c

2

+b

4

+b

2

c

2

⇒b

4

−2b

2

ac+a

2

c

2

=(b

2

−2ac)

2

=0

∴b

2

=ac

i.e. a,b,c are in GP.

Hence, option B.

HOPE IT HELPS YOU