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The equation whose roots are multiplied by 3 of those of $2 x^{3} - 3 x^{2} + 4 x - 5 = 0$ is

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2 x^{3} - 9 x^{2} + 36 x - 135 = 0

2 x^{3} - 9 x^{2} - 36 x + 135 = 0

x^{3} - 9 x^{2} + 36 x + 135 = 0

2 x^{3} - 9 x^{2} + 36 x + 135 = 0

answer is A.

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Detailed Solution

2 x^{3} - 3 x^{2} + 4 x - 5 = 0

$2 {(\frac{x}{3})}^{3} - 3 {(\frac{x}{3})}^{2} + 4 (\frac{x}{3}) - 5 = 0$

$2 (\frac{x^{3}}{27}) - 3 (\frac{x^{2}}{9}) + 4 (\frac{x}{3}) - 5 = 0$

$\frac{2 x^{3}}{27} - \frac{x^{2}}{3} + \frac{4 x}{3} - 5 = 0$

$2 x^{3} - 9 x^{2} + 36 x - 135 = 0$

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