Question

The equation whose roots are $2,1\pm 3i$ is

• A. $x^3-4x^2+14x-20=0$
• B. $x^3-x^2+5x-14=0$
• C. $x^3+2x^2-3x-10=0$
• D. $x^3-3x^2-14x+10=0$

Answer 1

The correct option is A $x^3-4x^2+14x-20=0$

Roots are $2,1+3i,1-3i$

Then Sum of roots $S_1=2+1+3i+1-3i=4$

$S_2=2\times (1+3i)+2\times (1-3i)+(1+3i)(1-3i)$

$=2+6i+2-6i+1-3i+3i+9=14$

$S_3=2\times (1+3i)\times (1-3i)=2(1+9)=20$

Hence using $x^3-S_1{x}^2+S_{2}x-S_3=0$ equation is $x^3-4x^2+14x-20=0$.