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Find the roots of the equation 3x² - 12x + 12 = 0. (2021)
Find the roots of the equation 3x² - 12x + 12 = 0. (2021)
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Q1
Find the roots of the equation 3x² - 12x + 12 = 0. (2021)
2
4
0
3
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Dividing by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the roots of the equation 3x² - 12x + 12 = 0. (2021)
Solution:
Dividing by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.
Steps: 7
Show Steps
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.
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