Find the Discriminant -3=x^2+4x+1

$- 3 = x^{2} + 4 x + 1$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$- 3 - x^{2} = 4 x + 1$

Subtract $4 x$ from both sides of the equation.

$- 3 - x^{2} - 4 x = 1$

Subtract $1$ from both sides of the equation.

$- 3 - x^{2} - 4 x - 1 = 0$

Subtract $1$ from $- 3$ .

$- x^{2} - 4 x - 4 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 4)}^{2} - 4 (- - 4)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 4$ to the power of $2$ .

$16 - 4 (- - 4)$

Multiply $- 4 (- - 4)$ .

Multiply $- 1$ by $- 4$ .

$16 - 4 \cdot 4$

Multiply $- 4$ by $4$ .

$16 - 16$

Subtract $16$ from $16$ .

$0$