Question

If a, b, c are in AP and if the equations (b−c)x2+(c−a)x+(a−b)=0 and 2(c+a)x2+(b+c)x=0 have a common root, then
which of them are in ap :
a) a2 b2 c2
b) a2 c2 b2
c) c2 a2 b2

Answer 1

◌⑅●♡⋆♡Answer♡⋆♡●⑅◌

Given x

2

+ax+bc=0 and x

2

+bx+ac=0 have a common root.

Let p be the common root of the given equations.

Then we've,

p

2

+ap+bc=0.....(1) and p

2

+pb+ac=0.....(2).

Now, (2)− (1) we get,

p(b−a)−c(b−a)=0

or, (b−a)(p−c)=0

or, p=c [ Since a



=b]

Now putting p=c in (1) we get,

c

2

+ac+bc=0

or, (c+a+b)=0 [ Since c



=0]

or, a+b+c=0.

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♥Mrs Shareef♥

Answer 2

Answer:

Hey..................