QQuestionMathematics
QuestionMathematics
If the discriminant of a quadratic equation is negative, how many real solutions does the equation have?
A. 0
B. 1
C. 2
D. 3
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Answer
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Step 1:I'll solve this step by step, following the LaTeX formatting guidelines precisely.
Step 2:: Recall the quadratic formula
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
Step 3:: Understand the discriminant
The term under the square root, $$b^{2} - 4ac$$, is called the discriminant.
Its value determines the number of real solutions.
Step 4:: Analyze the discriminant
- If $$b^{2} - 4ac < 0$$, there are 0 real solutions
- If b^{2} - 4ac = 0, there is 1 real solution (a repeated root)
Step 5:: Interpret a negative discriminant
When the discriminant is negative, $$\sqrt{b^{2} - 4ac}$$ becomes an imaginary number.
This means the solutions will be complex, not real.
Final Answer
A. 0 real solutions when the discriminant is negative.
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