Examples

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

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

Step 1

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

b^{2} - 4 (a c)

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

Step 2

Substitute in the values of

a

$a$ ,

b

$b$ , and

c

$c$ .

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

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

Step 3

Evaluate the result to find the discriminant.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raise

- 2

$- 2$ to the power of

2

$2$ .

4 - 4 (1 \cdot 4)

$4 - 4 (1 \cdot 4)$

Step 3.1.2

Multiply

- 4 (1 \cdot 4)

$- 4 (1 \cdot 4)$ .

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Step 3.1.2.1

Multiply

4

$4$ by

1

$1$ .

4 - 4 \cdot 4

$4 - 4 \cdot 4$

Step 3.1.2.2

Multiply

- 4

$- 4$ by

4

$4$ .

4 - 16

$4 - 16$

4 - 16

$4 - 16$

4 - 16

$4 - 16$

Step 3.2

Subtract

16

$16$ from

4

$4$ .

- 12

$- 12$

- 12

$- 12$

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