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Find the roots of the equation 4x² - 12x + 9 = 0. (2023)
Find the roots of the equation 4x² - 12x + 9 = 0. (2023)
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Q1
Find the roots of the equation 4x² - 12x + 9 = 0. (2023)
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This is a perfect square: (2x - 3)² = 0, hence the root is x = 1.5.
Questions & Step-by-step Solutions
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Q
Q: Find the roots of the equation 4x² - 12x + 9 = 0. (2023)
Solution:
This is a perfect square: (2x - 3)² = 0, hence the root is x = 1.5.
Steps: 8
Show Steps
Step 1: Start with the equation 4x² - 12x + 9 = 0.
Step 2: Notice that the equation can be factored. We want to express it as a perfect square.
Step 3: Rewrite the equation as (2x - 3)² = 0. This means we are looking for a number that, when squared, equals 0.
Step 4: Set the expression inside the square equal to 0: 2x - 3 = 0.
Step 5: Solve for x by adding 3 to both sides: 2x = 3.
Step 6: Divide both sides by 2 to find x: x = 3/2.
Step 7: Convert 3/2 to a decimal: x = 1.5.
Step 8: Therefore, the root of the equation is x = 1.5.
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