Precalculus Examples

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

Step 1

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

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

Step 2

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

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

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

$4 - 4 (1 \cdot 4)$

Step 3.1.2

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

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Step 3.1.2.1

Multiply $4$ by $1$ .

$4 - 4 \cdot 4$

Step 3.1.2.2

Multiply $- 4$ by $4$ .

$4 - 16$

Step 3.2

Subtract $16$ from $4$ .

$- 12$

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