solve the following equations by using Quadratic fomyla; \( x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \) \( x^{2}-6 x+9-0 \) how many roots are in the equation

To solve the equation \( x^{2}-6 x+9=0 \) using the quadratic formula, we first identify the coefficients: \( a = 1 \), \( b = -6 \), and \( c = 9 \). Plugging these values into the formula gives us \( x = \frac{-(-6) \pm \sqrt{(-6)^{2}-4(1)(9)}}{2(1)} \). Simplifying further, we find that the discriminant \( (-6)^{2}-4(1)(9) = 0 \), indicating that there is one unique root. In this specific case, the equation factors perfectly as \( (x-3)^2 = 0 \), which means it has a double root at \( x = 3 \). So, there's just one distinct solution, but it's counted twice!