Find the roots of the equation 3x^2 + 6x + 3 = 0.

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Question: Find the roots of the equation 3x^2 + 6x + 3 = 0.

Options:

Correct Answer: x = -1

Solution:

This can be simplified to x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, the root is x = -1.

Find the roots of the equation 3x^2 + 6x + 3 = 0.

Find the roots of the equation 3x^2 + 6x + 3 = 0.

Step 1: Start with the equation 3x^2 + 6x + 3 = 0.
Step 2: Divide every term in the equation by 3 to simplify it. This gives you x^2 + 2x + 1 = 0.
Step 3: Now, look for two numbers that multiply to 1 (the constant term) and add up to 2 (the coefficient of x). These numbers are 1 and 1.
Step 4: Rewrite the equation using these numbers: (x + 1)(x + 1) = 0.
Step 5: Set each factor equal to zero: x + 1 = 0.
Step 6: Solve for x by subtracting 1 from both sides: x = -1.

Quadratic Equations – Understanding how to solve quadratic equations using factoring and the quadratic formula.
Factoring – Recognizing how to factor a quadratic expression to find its roots.
Simplification – Simplifying equations to make them easier to solve.