Find the roots of each equation. 9y^2-30y+25=0

To find the roots of the quadratic equation \(9y^2 - 30y + 25 = 0\), we can use the quadratic formula:<br /><br />\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]<br /><br />Here, \(a = 9\), \(b = -30\), and \(c = 25\).<br /><br />First, calculate the discriminant (\(\Delta\)):<br /><br />\[ \Delta = b^2 - 4ac \]<br />\[ \Delta = (-30)^2 - 4 \cdot 9 \cdot 25 \]<br />\[ \Delta = 900 - 900 \]<br />\[ \Delta = 0 \]<br /><br />Since the discriminant is zero, there is one unique root. Now, substitute the values into the quadratic formula:<br /><br />\[ y = \frac{-(-30) \pm \sqrt{0}}{2 \cdot 9} \]<br />\[ y = \frac{30 \pm 0}{18} \]<br />\[ y = \frac{30}{18} \]<br />\[ y = \frac{5}{3} \]<br /><br />So, the root of the equation \(9y^2 - 30y + 25 = 0\) is:<br /><br />\[ y = \frac{5}{3} \]