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

x^{3} + 8 x^{2} + 20 x + 16 = 0

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x^{3} - 8 x^{2} - 20 x + 16 = 0

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x^{3} - 8 x^{2} + 20 x + 16 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{3} + 8 x^{2} - 20 x + 16 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $x^{3} + 8 x^{2} + 20 x + 16 = 0$
We know, the roots are diminished by $3$ .
In $x^{3} - x^{2} - x + 1 = 0$
Replacing $x \to x + 3$ , we get
${(x + 3)}^{3} - {(x + 3)}^{2} - (x + 3) + 1 = 0 \Rightarrow x^{3} + 8 x^{2} + 20 x + 16 = 0$

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