What are the roots of the equation 3x² - 12x + 12 = 0? (2019)

₹0.0

Question: What are the roots of the equation 3x² - 12x + 12 = 0? (2019)

Options:

Correct Answer: 4

Solution:

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

What are the roots of the equation 3x² - 12x + 12 = 0? (2019)

What are the roots of the equation 3x² - 12x + 12 = 0? (2019)

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 last number) and add up to -4 (the middle number). 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 – Understanding how to solve quadratic equations using factoring and the quadratic formula.
Factoring – Recognizing perfect square trinomials and factoring them correctly.
Roots of Equations – Identifying the roots of a quadratic equation and understanding their significance.