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For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
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Q1
For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
Real and distinct
Real and equal
Complex
None of the above
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The discriminant is 0 (b^2 - 4ac = 16 - 16 = 0), indicating real and equal roots.
Questions & Step-by-step Solutions
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Q: For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
Solution:
The discriminant is 0 (b^2 - 4ac = 16 - 16 = 0), indicating real and equal roots.
Steps: 6
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Step 1: Identify the coefficients in the quadratic equation x^2 + 4x + 4 = 0. Here, a = 1, b = 4, and c = 4.
Step 2: Use the formula for the discriminant, which is b^2 - 4ac.
Step 3: Calculate b^2: 4^2 = 16.
Step 4: Calculate 4ac: 4 * 1 * 4 = 16.
Step 5: Subtract the two results: 16 - 16 = 0.
Step 6: Interpret the result: Since the discriminant is 0, this means the roots are real and equal.
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