Question

what is the discriminant for
$x^2 + x + 1 = 0$?

enter only the numerical answer.

Explanation:

Step1: Recall the discriminant formula

For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(D\) is given by \(D = b^2 - 4ac\).

Step2: Identify coefficients

In the equation \(x^2 + x + 1 = 0\), we have \(a = 1\), \(b = 1\), and \(c = 1\).

Step3: Calculate the discriminant

Substitute the values of \(a\), \(b\), and \(c\) into the formula: \(D = (1)^2 - 4\times1\times1\)
\(= 1 - 4\)
\(= -3\)

Answer:

-3