Question

If a, b are the roots of the equation
(a) 1
(b) 2
(c) −1
(d) 3

Answer 1

(c) −1
Given equation: $x^2+x+1=0$
Also, $a$ and $b$ are the roots of the given equation.
Sum of the roots = $a+b=\frac{-C\mathrm{oefficient}\mathrm{of}x}{C\mathrm{oefficient}\mathrm{of}{x}^2}=-\frac{1}{1}=-1$

Product of the roots = $ab=\frac{C\mathrm{onstant}\mathrm{term}}{C\mathrm{oefficient}\mathrm{of}\mathit{}{x}^2}=\frac{1}{1}=1$

$$\begin{gathered} \therefore (a+b{)}^2=a^2+b^2+2ab \\ \Rightarrow (-1{)}^2=a^2+b^2+2\times 1 \\ \Rightarrow 1-2=a^2+b^2 \\ \Rightarrow a^2+b^2=-1 \end{gathered}$$