Question

If the roots of $x^3-42x^2+336x-512=0$, are in increasing geometric progression, then its common ratio is

• A. 2: 1
• B. 3: 1
• C. 4: 1
• D. 6: 1

Answer 1

Answer: (C)

Given, cubic equation is
$x^3-42x^2+336x-512=0$
$\Rightarrow x^2(x-2)-40x(x-2)+256(x-2)=0$
$\Rightarrow (x-2)\left(x^2-40x+256\right)=0$
$\Rightarrow (x-2)\left\{x^2-32x-8x+256\right\}=0$
$\Rightarrow (x-2)\{x(x-32)-8(x-32)\}=0$
$\Rightarrow (x-2)(x-32)(x-8)=0$
$\Rightarrow (x-2)(x-8)(x-32)=0$
$\Rightarrow x=2,8,32$
Which represents a geometric progression in increasing order.
Common ratio $=\frac{8}{2}=4:1$