Question:
If \( x^2 - 4x + 4 = 0 \), what is the sum of the roots?
If \( x^2 - 4x + 4 = 0 \), what is the sum of the roots?
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For quadratic equations of the form \( ax^2 + bx + c = 0 \), the sum of the roots can be found using the formula \( -\frac{b}{a} \). In this case, \( b = -4 \) and \( a = 1 \), so the sum of the roots is \( -\frac{-4}{1} = 4 \).
Updated On: Oct 6, 2025
- \( -4 \)
- \( -2 \)
- \( 0 \)
- \( 2 \)
- \( 4 \)
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Solution and Explanation
The given quadratic equation is \( x^2 - 4x + 4 = 0 \).
Step 1: This is a perfect square trinomial, which can be factored as:
\[
(x - 2)^2 = 0.
\]
Step 2: Solving for \( x \), we get:
\[
x - 2 = 0
\Rightarrow
x = 2. \] Step 3: Since both roots are \( x = 2 \), the sum of the roots is: \[ 2 + 2 = 4. \] Thus, the sum of the roots is \( 4 \).
\Rightarrow
x = 2. \] Step 3: Since both roots are \( x = 2 \), the sum of the roots is: \[ 2 + 2 = 4. \] Thus, the sum of the roots is \( 4 \).
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