If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the

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Question: If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the roots?

Options:

Correct Answer: Real and equal

Solution:

The discriminant is 0, indicating that the roots are real and equal.

If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the roots?

If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the roots?

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.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to identify its coefficients.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation.
Nature of Roots – Roots can be real and distinct, real and equal, or complex based on the value of the discriminant.