In the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have?

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Question: In the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have?

Options:

Correct Answer: Real and equal

Solution:

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

In the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have?

In the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have?

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 formula: D = (6)^2 - 4(1)(9).
Step 6: Calculate (6)^2, which is 36.
Step 7: Calculate 4(1)(9), which is 36.
Step 8: Subtract the two results: D = 36 - 36 = 0.
Step 9: Interpret the discriminant: Since D = 0, the roots are real and equal.

Quadratic Equation – A polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
Discriminant – The value calculated as b^2 - 4ac, which determines the nature of the roots of a quadratic equation.
Types of Roots – Roots can be real and distinct, real and equal, or complex, depending on the value of the discriminant.