Question

what is the value of the discriminant for the quadratic equation 0 = x + 2 + x²?
discriminant = b² - 4ac
○ −9
○ −7
○ 7
○ 9

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\). Given the equation \(0=x + 2+x^{2}\), we can rewrite it as \(x^{2}+x + 2=0\). Here, \(a = 1\), \(b = 1\), and \(c = 2\).

Step2: Apply the discriminant formula

The discriminant formula is \(D=b^{2}-4ac\). Substitute \(a = 1\), \(b = 1\), and \(c = 2\) into the formula:
\(D=(1)^{2}-4\times1\times2\)
\(D = 1-8\)
\(D=-7\)

Answer:

\(-7\) (corresponding to the option: \(-7\))