The polynomial equation of degree 5 whose roo | vedclass

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(B) To find the polynomial whose roots are translated by $-2$,we replace $x$ with $(x+2)$ in the original equation $x^5-2x^4+3x^3-4x^2+5x-6=0$. Substi

Vedclass · Accepted Answer

$x^5+8x^4+27x^3+46x^2+41x+12=0$

Vedclass · Answer

(B) To find the polynomial whose roots are translated by $-2$,we replace $x$ with $(x+2)$ in the original equation $x^5-2x^4+3x^3-4x^2+5x-6=0$. Substituting $x 	o x+2$: $(x+2)^5 - 2(x+2)^4 + 3(x+2)^3 - 4(x+2)^2 + 5(x+2) - 6 = 0$. Expanding each term: $(x^5+10x^4+40x^3+80x^2+80x+32) - 2(x^4+8x^3+24x^2+32x+16) + 3(x^3+6x^2+12x+8) - 4(x^2+4x+4) + 5(x+2) - 6 = 0$. Grouping like terms: $x^5 + (10-2)x^4 + (40-16+3)x^3 + (80-48+18-4)x^2 + (80-64+36-16+5)x + (32-32+24-16+10-6) = 0$. Simplifying the coefficients: $x^5 + 8x^4 + 27x^3 + 46x^2 + 41x + 12 = 0$.

The polynomial equation of degree $5$ whose roots are the translates of the roots of $x^5-2x^4+3x^3-4x^2+5x-6=0$ by $-2$ is:

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