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If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the
If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the roots?
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Q1
If the quadratic equation x^2 + 6x + 9 = 0 is solved, 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, indicating that the roots are real and equal.
Questions & Step-by-step Solutions
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Q
Q: If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the roots?
Solution:
The discriminant is 0, indicating that the roots are real and equal.
Steps: 8
Show Steps
Step 1: Identify the quadratic equation, which is x^2 + 6x + 9 = 0.
Step 2: Recognize the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
Step 3: Identify the coefficients: a = 1, b = 6, c = 9.
Step 4: Calculate the discriminant using the formula D = b^2 - 4ac.
Step 5: Substitute the values into the discriminant formula: D = (6)^2 - 4(1)(9).
Step 6: Calculate (6)^2 = 36 and 4(1)(9) = 36.
Step 7: Now, find D: D = 36 - 36 = 0.
Step 8: Interpret the result: Since the discriminant D is 0, the roots are real and equal.
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