Find the polynomial equation whose roots are the translates of the roots of the equation $x^{5} - 4 x^{4} + 3 x^{2} - 4 x + 6 = 0$ by $- 3$ .

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Solution

Every root of equation will increase by $- 3$ inorder to get new roots
If we replace $x$ with $x + 3$ in old equation , then we will get new equation.
Therefore the new equation will be ${(x + 3)}^{5} - 4 {(x + 3)}^{4} + 3 {(x + 3)}^{2} - 4 (x + 3) + 6 = 0$

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