Question

what is the value of the discriminant for the quadratic equation $-3 = -x^2 + 2x$?
discriminant $= b^2 - 4ac$
\bigcirc $-8$
\bigcirc $4$
\bigcirc $8$
\bigcirc $16

Explanation:

Step1: Rewrite the equation in standard form

First, we need to rewrite the quadratic equation \(-3 = -x^2 + 2x\) in the standard form \(ax^2 + bx + c = 0\). By adding \(x^2\) and subtracting \(2x\) from both sides, we get:
\(x^2 - 2x - 3 = 0\)
Here, \(a = 1\), \(b = -2\), and \(c = -3\).

Step2: Calculate the discriminant

The formula for the discriminant is \(D = b^2 - 4ac\). Substitute \(a = 1\), \(b = -2\), and \(c = -3\) into the formula:
\[

$$\begin{align*} D&= (-2)^2 - 4(1)(-3)\\ &= 4 + 12\\ &= 16 \end{align*}$$

\]

Answer:

16