The equation whose roots are diminished by $1$ than those of $4 x^{3} - x^{2} + 2 x - 3 = 0$ , is:

4 x^{3} - 11 x^{2} + 12 x + 2 = 0

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4 x^{3} - 11 x^{2} + 12 x - 3 = 0

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4 x^{3} + 11 x^{2} + 12 x + 2 = 0

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4 x^{3} + 11 x^{2} + 12 x - 3 = 0

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Solution

The correct option is B $4 x^{3} + 11 x^{2} + 12 x + 2 = 0$
The equation whose roots are $α, β$ and $γ$ is $f (x) = 0$ (say)
The equation whose roots are $α - 1, β - 1$ and $γ - 1$ is $f (x + 1) = 0$
Thus, we put $x + 1$ in the place of $x$ in above expression to get the answer.

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Similar questions

\int \frac{x^{4} + 4 x^{3} + 11 x^{2} + 12 x + 8}{(x^{2} + 2 x + 3)^{2} (x + 1)} d x

x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36 = 0

4 x^{3} - 6 x^{2} + 12 x + 9 = 0

x^{4} + 4 x^{3} - 2 x^{2} - 12 x + k = 0

3 x^{3} + 11 x^{2} + 12 x + 4 = 0

(- 1)

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