Examples

2 x^{2} + 1 = 0

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

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

$c$ .

0^{2} - 4 (2 \cdot 1)

$0^{2} - 4 (2 \cdot 1)$

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

Raising

0

$0$ to any positive power yields

0

$0$ .

0 - 4 (2 \cdot 1)

$0 - 4 (2 \cdot 1)$

Step 3.1.2

Multiply

- 4 (2 \cdot 1)

$- 4 (2 \cdot 1)$ .

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Step 3.1.2.1

Multiply

2

$2$ by

1

$1$ .

0 - 4 \cdot 2

$0 - 4 \cdot 2$

Step 3.1.2.2

Multiply

- 4

$- 4$ by

2

$2$ .

0 - 8

$0 - 8$

0 - 8

$0 - 8$

0 - 8

$0 - 8$

Step 3.2

Subtract

8

$8$ from

0

$0$ .

- 8

$- 8$

- 8

$- 8$

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