The quadratic equation x^2 + 6x + 9 = 0 has roots that are:

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Question: The quadratic equation x^2 + 6x + 9 = 0 has roots that are:

Options:

Correct Answer: Real and equal

Solution:

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

The quadratic equation x^2 + 6x + 9 = 0 has roots that are:

The quadratic equation x^2 + 6x + 9 = 0 has roots that are:

Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c = 0. Here, a = 1, b = 6, and c = 9.
Step 2: Calculate the discriminant using the formula D = b^2 - 4ac. Substitute the values: D = 6^2 - 4(1)(9).
Step 3: Simplify the calculation: D = 36 - 36 = 0.
Step 4: Interpret the discriminant. Since D = 0, it means the quadratic equation has real and equal roots.
Step 5: Conclude that the roots of the equation x^2 + 6x + 9 = 0 are real and equal.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to find its roots using the discriminant.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation.
Real and Equal Roots – When the discriminant is zero, the quadratic equation has exactly one real root, which is repeated.