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In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
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In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
Real and distinct
Real and equal
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The discriminant is 0 (b² - 4ac = 0), indicating that the roots are real and equal.
Questions & Step-by-step Solutions
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Q: In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
Solution:
The discriminant is 0 (b² - 4ac = 0), indicating that the roots are real and equal.
Steps: 6
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Step 1: Identify the coefficients in the quadratic equation x² + 6x + 9 = 0. Here, a = 1, b = 6, and c = 9.
Step 2: Use the formula for the discriminant, which is b² - 4ac.
Step 3: Calculate b²: 6² = 36.
Step 4: Calculate 4ac: 4 * 1 * 9 = 36.
Step 5: Subtract the two results: 36 - 36 = 0.
Step 6: Since the discriminant is 0, this means the roots are real and equal.
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