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

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

Options:

Correct Answer: x = -1

Solution:

Dividing the equation by 3 gives x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, x = -1.

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

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

Step 1: Start with the quadratic equation: 3x^2 + 6x + 3 = 0.
Step 2: Divide the entire equation by 3 to simplify it: 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).
Step 4: The numbers that work are 1 and 1, so we can factor the equation: (x + 1)(x + 1) = 0.
Step 5: Set each factor equal to zero: x + 1 = 0.
Step 6: Solve for x: x = -1.
Step 7: Since both factors are the same, the root is x = -1 with a multiplicity of 2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, completing the square, or the quadratic formula.
Factoring – Recognizing how to factor a quadratic expression into binomials.
Roots of Equations – Finding the values of x that satisfy the equation, also known as the solutions or roots.