Find the Discriminant x(x-2)+1=0

$x (x - 2) + 1 = 0$

Step 1

Simplify the left side.

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 1 = 0$

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 + 1 = 0$

Move $- 2$ to the left of $x$ .

$x^{2} - 2 x + 1 = 0$

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 $c$ .

${(- 2)}^{2} - 4 (1 \cdot 1)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (1 \cdot 1)$

Multiply $- 4 (1 \cdot 1)$ .

Multiply $1$ by $1$ .

$4 - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$4 - 4$

Subtract $4$ from $4$ .

$0$