Algebra Examples

$x^{2} + 81$

Find the discriminant for $x^{2} + 81 = 0$ . In this case, $b^{2} - 4 a c = - 324$ .

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

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

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

$0^{2} - 4 (1 \cdot 81)$

Evaluate the result to find the discriminant.

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Simplify each term.

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Raising $0$ to any positive power yields $0$ .

$0 - 4 (1 \cdot 81)$

Multiply $81$ by $1$ .

$0 - 4 \cdot 81$

Multiply $- 4$ by $81$ .

$0 - 324$

Subtract $324$ from $0$ .

$- 324$

A perfect square number is an integer that is the square of another integer. $\sqrt{- 324} \approx 18 i$ , which is not an integer number.

$\sqrt{- 324} \approx 18 i$

Since $- 324$ can't be the square of another integer, it is not a perfect square number.

The polynomial $x^{2} + 81$ is prime because the discriminant is not a perfect square number.

Prime