Find the Discriminant 0=x^2-4x+10

$0 = x^{2} - 4 x + 10$

Step 1

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

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

$- x^{2} = - 4 x + 10$

Add $4 x$ to both sides of the equation.

$- x^{2} + 4 x = 10$

Subtract $10$ from both sides of the equation.

$- x^{2} + 4 x - 10 = 0$

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 $c$ .

$4^{2} - 4 (- - 10)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$16 - 4 (- - 10)$

Multiply $- 4 (- - 10)$ .

Multiply $- 1$ by $- 10$ .

$16 - 4 \cdot 10$

Multiply $- 4$ by $10$ .

$16 - 40$

Subtract $40$ from $16$ .

$- 24$