Question

The equation whose roots are $0,0,2,2,-2,-2$, is

• A. $x^6+8x^4-16x^2=0$
• B. $x^6-4x^4-16x^2=0$
• C. $x^6-8x^4+16x^2=0$
• D. $x^6+4x^4+16x^2=0$

Answer 1

The correct option is C $x^6-8x^4+16x^2=0$

It is given that the roots are $0,0,2,2,-2,-2$

Hence, the equation is

$(x-0)(x-0)(x-2)(x-2)(x+2)(x+2)=0$

$x^2(x-2{)}^2(x+2{)}^2=0$

$x^2\left[\right(x-2\left)\right(x+2\left)\right]\left[\right(x-2\left)\right(x+2\left)\right]=0$

$x^2(x^2-4)(x^2-4)=0$

$x^2[x^4-8x^2+16]=0$

$x^6-8x^4+16x^2=0$