If the equations ax + 4y + z = 0, bx + 3y + z=0, cx + 2y + z = 0 have non-trivial solution, then a, b, c are in

Question

If the equations ax + 4y + z = 0, bx + 3y + z=0, cx + 2y + z = 0 have non-trivial solution, then a, b, c are in (A) A.P. (B) G.P. (C) A.G.P. (D) None of these

Tardigrade Admin · Accepted Answer

| beginmatrixa&4&1 b&3&1 c&2&1 endmatrix|=0 ⇒ a(3-2)-4 (b-c)+1(2b-3c)=0 ⇒ a-2b+c=0 ⇒ 2b=a+c Hence, a, b, c are in A.P.

Q. If the equations $a x + 4 y + z = 0$ , $b x + 3 y + z = 0$ , $c x + 2 y + z = 0$ have non-trivial solution, then $a, b, c$ are in

$A . P .$

$G . P .$

$A . G . P .$

None of these

$∣ ∣ a b c 432111 ∣ ∣ = 0 \Rightarrow a (3 - 2) - 4 (b - c) + 1 (2 b - 3 c) = 0$
$\Rightarrow a - 2 b + c = 0 \Rightarrow 2 b = a + c$
Hence, a, b, c are in A.P.

Q. If the equations ax+4y+z=0, bx+3y+z=0, cx+2y+z=0 have non-trivial solution, then a,b,c are in

A.P.

G.P.

A.G.P.