Find the roots of the quadratic equation x^2 + 4x + 4 = 0.

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Question: Find the roots of the quadratic equation x^2 + 4x + 4 = 0.

Options:

Correct Answer: {-2}

Solution:

The equation factors to (x + 2)(x + 2) = 0, giving a double root x = -2.

Find the roots of the quadratic equation x^2 + 4x + 4 = 0.

Find the roots of the quadratic equation x^2 + 4x + 4 = 0.

Step 1: Write down the quadratic equation: x^2 + 4x + 4 = 0.
Step 2: Look for two numbers that multiply to 4 (the last number) and add to 4 (the middle number).
Step 3: The numbers that work are 2 and 2, because 2 * 2 = 4 and 2 + 2 = 4.
Step 4: Rewrite the equation using these numbers: (x + 2)(x + 2) = 0.
Step 5: Set each factor equal to zero: x + 2 = 0.
Step 6: Solve for x: x = -2.
Step 7: Since both factors are the same, we have a double root at x = -2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, the quadratic formula, or completing the square.
Factoring – Recognizing how to factor a quadratic expression into the product of two binomials.
Roots of Equations – Identifying the solutions (roots) of a quadratic equation and understanding the significance of double roots.