College Algebra : Solutions and Solution Sets

Study concepts, example questions & explanations for College Algebra

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Example Questions

Example Question #2 :How To Find A Solution Set

Give all real solutions of the following equation:

Possible Answers:

Correct answer:

Explanation:

By substituting- and, subsequently,this can be rewritten as a quadratic equation, and solved as such:

We are looking to factor the quadratic expression as, replacing the two question marks with integers with productand sum 5; these integers are.

Substitute back:

The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:

Set each factor to zero and solve:

Since no real number squared is equal to a negative number, no real solution presents itself here.

The solution set is.

Example Question #11 :How To Find A Solution Set

Give all real solutions of the following equation:

Possible Answers:

The equation has no real solutions.

Correct answer:

Explanation:

By substituting- and, subsequently,this can be rewritten as a quadratic equation, and solved as such:

We are looking to factor the quadratic expression as, replacing the two question marks with integers with product 36 and sum; these integers are.

Substitute back:

These factors can themselves be factored as the difference of squares:

Set each factor to zero and solve:

The solution set is.

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