The roots of the equation 4x^2 - 12x + 9 = 0 are: (2019)

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Question: The roots of the equation 4x^2 - 12x + 9 = 0 are: (2019)

Options:

Correct Answer: 3 and 3

Exam Year: 2019

Solution:

The equation can be factored as (2x - 3)(2x - 3) = 0, hence the roots are 3 and 3.

The roots of the equation 4x^2 - 12x + 9 = 0 are: (2019)

The roots of the equation 4x^2 - 12x + 9 = 0 are: (2019)

Step 1: Start with the equation 4x^2 - 12x + 9 = 0.
Step 2: Look for a way to factor the equation. Notice that 4x^2 can be written as (2x)^2.
Step 3: Rewrite the equation as (2x)^2 - 12x + 9 = 0.
Step 4: Identify the middle term -12x. We can express it as -3(2x) - 3(2x).
Step 5: Rewrite the equation as (2x - 3)(2x - 3) = 0.
Step 6: Set each factor equal to zero: 2x - 3 = 0.
Step 7: Solve for x by adding 3 to both sides: 2x = 3.
Step 8: Divide both sides by 2: x = 3/2.
Step 9: Since both factors are the same, the root is repeated: x = 3/2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring and the quadratic formula.
Roots of Equations – Identifying and calculating the roots of a quadratic equation.
Factoring – The process of expressing a quadratic equation as a product of its factors.