1. a1, b1, c1 are in

Question

Let the equation ax² + 2bx + c = 0 and a₁x₂ + 2b₁x + c₁ = 0 have a common root and (a, b, c, a₁, b₁,c₁ ∈ R). If a/a₁,b/b₁,c/c₁ are in AP, then

1.  a₁, b₁, c₁ are in

(A) AP

(B) GP

(C) HP

(D) None of these

2.  The value of the common root is

(A)  −c₁/a₁

(B)  -b₁/a₁

(C)  - c₁/b₁

(D)   -b₁/c₁

3.  If  b/b₁ ,a/a₁,c/c₁ are in HP, then

(A)  a, − 4b, −2c are in GP

(B)  2a, − 4b, − c are in GP

(C)  a, c, −b are in GP

(D)  None of these

Answer 1

Correct option 1. (B) 2. (C)3.  (A)

1.

  

Since,

a/a₁ ,b/b₁,c/c₁ are in AP.

Hence, a1, b1, c1 are in GP. 

2.

3.

 

Hence, -a/4,b,c/2  are in GP or a, - 4b, -2c are in GP.