Precalculus Examples

$- 5 x^{2} - 4 x + 1 = 0$

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 $c$ .

${(- 4)}^{2} - 4 (- 5 \cdot 1)$

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

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

$16 - 4 (- 5 \cdot 1)$

Step 3.1.2

Multiply $- 4 (- 5 \cdot 1)$ .

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Step 3.1.2.1

Multiply $- 5$ by $1$ .

$16 - 4 \cdot - 5$

Step 3.1.2.2

Multiply $- 4$ by $- 5$ .

$16 + 20$

Step 3.2

Add $16$ and $20$ .

$36$