Question

The equation whose roots are diminished by $2$ than those of $x^4-5x^3+7x^2-17x+11=0$, is:

• A. $x^4+3x^3-x^2-17x-19=0$
• B. $x^4+3x^3+x^2-17x-19=0$
• C. $x^4+3x^3+x^2+17x-19=0$
• D. $x^4+3x^3-x^2+17x-19=0$

Answer 1

The correct option is B $x^4+3x^3+x^2-17x-19=0$

Given equation is $x^4-5x^3+7x^2-17x+11=0$
Replacing $x\to x+2$, we get
${(x+2)}^4-5{(x+2)}^3+7{(x+2)}^2-17(x+2)+11=0$

$\Rightarrow (x+2{)}^2(x+2{)}^2-5(x+2{)}^3+7(x^2+4x+4)-17x-34+11=0$

$\Rightarrow x^4+3x^3+x^2-17x-19=0$