Question

The equation whose roots are the squares of the roots of equation $x^2-x+1=0$ is

• A. $x^2-x+1=0$
• B. $x^2+x+1=0$
• C. $x^2-x-1=0$
• D. $-x^2-x-1=0$

Answer 1

The correct option is B $x^2+x+1=0$

The given equation is $x^2-x+1=0$ ....... (1)
Here, $a+\beta =1$ and $a\beta =1$. Therefore,
$a^2+{\beta }^2=(a+\beta {)}^2-2a\beta =1-2=-1$
and $a^2{\beta }^2=(a\beta {)}^2=1^2=0$
Therefore, the equation whose roots are square of 1 is $x^2$ -(sum of the roots)x +product $=0$
or $x^2-(-1)x+1=0$
or $x^2+x+1=0$