Precalculus Examples

Find the discriminant for . In this case, .
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The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
Substitute in the values of , , and .
Evaluate the result to find the discriminant.
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Simplify each term.
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Raising to any positive power yields .
Multiply by .
Multiply by .
Add and .
A perfect square number is an integer that is the square of another integer. , which is not an integer number.
Since can't be the square of another integer, it is not a perfect square number.
The polynomial is prime because the discriminant is not a perfect square number.
Prime
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