Question

The transformed equation of $x^3-\frac{5}{2}{x}^2-\frac{7}{18}x+\frac{1}{108}=0$ by removing fractional coefficients is

• A. $x^3-15x^2+14x-2=0$
• B. $x^3-15x^2-14x-2=0$
• C. $x^3-15x^2+14x+2=0$
• D. $x^3-15x^2-14x+2=0$

Answer 1

Answer: (D)

$x^3-15x^2-14x+2=0$

The given equation is $x^3-\frac{5}{2}{x}^2-\frac{7}{18}x+\frac{1}{108}=0$ ...(1)
Multiplying the roots of the given equation by $m$, the transformed equation is
$x^3-\frac{5}{2}m{x}^2-\frac{7}{18}{m}^{2}x+\frac{1}{108}{m}^3=0$
$\Rightarrow x^3-\frac{5}{2}m{x}^2-\frac{7}{2.3^2}{m}^{2}x+\frac{1}{2^2.3^3}{m}^3=0$ ...(2)
Clearly the least value of m to remove the fractional coefficient is $m=2.3=6$
Therefore putting $m=2.3$ is (2), we get
$\Rightarrow x^3-\frac{5}{2}\left(2.3\right)x^2-\frac{7}{2.3^2}{\left(2.3\right)}^{2}x+\frac{1}{2^2.3^3}{\left(2.3\right)}^3=0\Rightarrow x^3-15x^2-14x+2=0$