Find the solution(s) using the quadratic formula.
$4x^2-4x+1=0$

• A. $x=\frac12$
• B. $x=-\frac12$
• C. $x=1,x=\frac12$
• D. $x=1,x=-\frac12$

Answer: (A)

Verified step by step guidance

1. Identify the coefficients from the quadratic equation \$4x^2 - 4x + 1 = 0\(. Here, \)a = 4\(, \)b = -4\(, and \)c = 1$.
2. Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), which is used to find the roots of any quadratic equation.
3. Calculate the discriminant \(\Delta = b^2 - 4ac\) by substituting the values: \(\Delta = (-4)^2 - 4 \times 4 \times 1\).
4. Evaluate the square root of the discriminant \(\sqrt{\Delta}\) and then substitute all values back into the quadratic formula to get the two possible solutions for \(x\).
5. Simplify the expressions for both \(x = \frac{-b + \sqrt{\Delta}}{2a}\) and \(x = \frac{-b - \sqrt{\Delta}}{2a}\) to find the exact roots of the equation.