Question

If $a,b$ are the roots of the equation, $x^2+x+1=0$, then $a^2+b^2=$

Answer 1

Given: $a,b$ are the roots of the equation,

$x^2+x+1=0$

Now,

$\text{sum of roots}=-\frac{\text{coefficient of x}}{\text{coefficient of}{x}^2}$

$\Rightarrow a+b=-1\dots \left(1\right)$

$\text{Product of roots}=\frac{\text{constant term}}{\text{coefficient of}{x}^2}$

$\Rightarrow ab=1\dots \left(2\right)$

We know

$(a+b{)}^2=a^2+b^2+2ab$

From equation $\left(1\right)$ and $\left(2\right)$, we get

$\Rightarrow (-1{)}^2=a^2+b^2+2$

$\Rightarrow a^2+b^2=1-2=-1$

Hence, option (C) is correct.