Find the roots of the quadratic equation 3x^2 - 12x = 0.

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Question: Find the roots of the quadratic equation 3x^2 - 12x = 0.

Options:

Correct Answer: x = 0, 4

Solution:

Factoring gives 3x(x - 4) = 0. Thus, x = 0 and x = 4.

Find the roots of the quadratic equation 3x^2 - 12x = 0.

Find the roots of the quadratic equation 3x^2 - 12x = 0.

Step 1: Start with the quadratic equation: 3x^2 - 12x = 0.
Step 2: Factor out the common term from both parts of the equation. Here, the common term is 3x.
Step 3: Rewrite the equation as: 3x(x - 4) = 0.
Step 4: Set each factor equal to zero. First, set 3x = 0.
Step 5: Solve for x in the first equation: 3x = 0 gives x = 0.
Step 6: Now set the second factor equal to zero: x - 4 = 0.
Step 7: Solve for x in the second equation: x - 4 = 0 gives x = 4.
Step 8: The roots of the equation are x = 0 and x = 4.

Quadratic Equations – Understanding how to solve quadratic equations using factoring.
Factoring – Recognizing how to factor a quadratic expression to find its roots.
Zero Product Property – Applying the zero product property to determine the values of x that satisfy the equation.