First slide

Theory of equations

Question

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

Difficult

A

$x^{3} - 3 x^{2} - x + 12 = 0$
B

$x^{3} - 3 x^{2} - x + 6 = 0$
C

$x^{3} - 3 x^{2} - 24 x - 216 = 0$
D

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

Solution

$2,2 \times 3^{2}, 2^{2} \times 3^{3}$
$m = 2 \times 3$
Transformed Equation whose roots are multiplied by 6 is $f (\frac{x}{6}) = {(\frac{x}{6})}^{3} - \frac{5}{2} {(\frac{x}{6})}^{2} - \frac{7}{18} (\frac{x}{6}) + \frac{1}{108} = 0 \Rightarrow x^{3} - 15 x^{2} - 14 x + 2 = 0$

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