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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.