Find the roots of the equation 3x² - 12x + 12 = 0. (2021)

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Question: Find the roots of the equation 3x² - 12x + 12 = 0. (2021)

Options:

Correct Answer: 2

Exam Year: 2021

Solution:

Dividing by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.

Find the roots of the equation 3x² - 12x + 12 = 0. (2021)

Find the roots of the equation 3x² - 12x + 12 = 0. (2021)

Step 1: Start with the equation 3x² - 12x + 12 = 0.
Step 2: Divide the entire equation by 3 to simplify it. This gives you x² - 4x + 4 = 0.
Step 3: Now, look for two numbers that multiply to 4 (the constant term) and add up to -4 (the coefficient of x). These numbers are -2 and -2.
Step 4: Rewrite the equation using these numbers: (x - 2)(x - 2) = 0.
Step 5: This can be written as (x - 2)² = 0.
Step 6: To find the root, set (x - 2) = 0. This gives you x = 2.
Step 7: Therefore, the root of the equation is 2.

Quadratic Equations – The question tests the ability to solve a quadratic equation using factoring and the quadratic formula.
Factoring – The solution involves recognizing that the quadratic can be factored into a perfect square.
Roots of Equations – The question assesses understanding of finding roots and their multiplicity.