College Algebra : Solutions and Solution Sets

Study concepts, example questions & explanations for College Algebra

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Example Questions

Example Question #1 : Solutions And Solution Sets

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 product  and 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 #1482 : Algebra Ii

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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