Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + x + 1 = 0$$
A) $\left\{ \frac { - 1 \pm i \sqrt { 3 } } { 2 } \right\}$
B) $\left\{ \frac { 1 \pm i \sqrt { 3 } } { 2 } \right\}$
C) $\left\{ \frac { 1 \pm \sqrt { 3 } } { 2 } \right\}$
D) $\left\{ \frac { - 1 \pm \sqrt { 3 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

To make $x^2 + x + 1$ a perfect square trinomial, we need to add $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$ to it, making it $x^2 + x + \frac{1}{4}$. This can be factored as $\left(x + \frac{1}{2}\right)^2$. However, the question seems to be incorrectly asking for the roots of the equation $x^2 + x + 1 = 0$, which are complex numbers, correctly given in option A.

Determine the Constant That Should Be Added to the Binomial x2+x+1=0x ^ { 2 } + x + 1 = 0x2+x+1=0

Determine the Constant That Should Be Added to the Binomial $x ^ { 2 } + x + 1 = 0$