Find the roots of each equation. 16x^2-8x+1=0

To find the roots of the quadratic equation \(16x^2 - 8x + 1 = 0\), we can use the quadratic formula:<br /><br />\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]<br /><br />Here, \(a = 16\), \(b = -8\), and \(c = 1\).<br /><br />First, calculate the discriminant (\(\Delta\)):<br /><br />\[ \Delta = b^2 - 4ac \]<br />\[ \Delta = (-8)^2 - 4 \cdot 16 \cdot 1 \]<br />\[ \Delta = 64 - 64 \]<br />\[ \Delta = 0 \]<br /><br />Since the discriminant is zero, there is one repeated root. Now, apply the quadratic formula:<br /><br />\[ x = \frac{-(-8) \pm \sqrt{0}}{2 \cdot 16} \]<br />\[ x = \frac{8 \pm 0}{32} \]<br />\[ x = \frac{8}{32} \]<br />\[ x = \frac{1}{4} \]<br /><br />So, the root of the equation \(16x^2 - 8x + 1 = 0\) is:<br /><br />\[ x = \frac{1}{4} \]