Find the roots of the equation 4x² - 12x + 9 = 0. (2023)

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Question: Find the roots of the equation 4x² - 12x + 9 = 0. (2023)

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

This is a perfect square: (2x - 3)² = 0, hence the root is x = 1.5.

Find the roots of the equation 4x² - 12x + 9 = 0. (2023)

Find the roots of the equation 4x² - 12x + 9 = 0. (2023)

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.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, completing the square, or the quadratic formula.
Perfect Squares – Recognizing and manipulating perfect square trinomials.