If a, b, c are in A.P., then the determinant |(x+2,x+3,x+2a)(x+3,x+4,x+2b)(x+4,x+5,x+2c)|

Question

Mark the correct alternative in the following :

If a, b, c are in A.P., then the determinant \(\begin{vmatrix} x+2 & x+3 & x+2a \\[0.3em] x+3 & x+4 & x+2b \\[0.3em] x+4 & x+5 & x+2c \end{vmatrix}\)

A. 0 

B. 1 

C. x 

D. 2x

Answer 1

Correct answer : (A)

Δ =\(\begin{vmatrix} x+2 & x+3 & x+2a \\[0.3em] x+3 & x+4 & x+2b \\[0.3em] x+4 & x+5 & x+2c \end{vmatrix}\)

{a + c = 2b} 

R₁→ R₁ – R₂ 

R₂→ R₂ – R₃