All HiSET: Math Resources
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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