Algebra Examples

$x^{2} + x - 20$

Step 1

Find the discriminant for $x^{2} + x - 20 = 0$ . In this case, $b^{2} - 4 a c = 81$ .

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Step 1.1

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

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

Step 1.2

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

$1^{2} - 4 (1 \cdot - 20)$

Step 1.3

Evaluate the result to find the discriminant.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

One to any power is one.

$1 - 4 (1 \cdot - 20)$

Step 1.3.1.2

Multiply $- 4 (1 \cdot - 20)$ .

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Step 1.3.1.2.1

Multiply $- 20$ by $1$ .

$1 - 4 \cdot - 20$

Step 1.3.1.2.2

Multiply $- 4$ by $- 20$ .

$1 + 80$

Step 1.3.2

Add $1$ and $80$ .

$81$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{81} = 9$ , which is an integer number.

$\sqrt{81} = 9$

Step 3

Since $81$ is the square of $9$ , it is a perfect square number.

$81$ is a perfect square number

Step 4

The polynomial $x^{2} + x - 20$ is not prime because the discriminant is a perfect square number.

Not prime