HiSET: Math : Quadratic equations

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #21 : Algebraic Concepts

Give the nature of the solution set of the equation

Possible Answers:

One imaginary solution

One rational solution

Two irrational solutions

Two imaginary solutions

Two rational solutions

Correct answer:

Two irrational solutions

Explanation:

To determine the nature of the solution set of a quadratic equation, it is necessary to first express it in standard form 

This can be done by subtracting 34 from to both sides:

The key to determining the nature of the solution set is to examine the discriminant 

. Setting , the value of the discriminant is

.

The discriminant is a positive number but not a perfect square. Therefore, there are two irrational solutions.

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