Question
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
Ask by Higgins Collins. in South Africa
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation \( x^{2}-6x+9=0 \) has one root: \( x=3 \).
Solution
Solve the equation \( x^{2}-6x+9=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-6x+9=0\)
- step1: Factor the expression:
\(\left(x-3\right)^{2}=0\)
- step2: Simplify the expression:
\(x-3=0\)
- step3: Move the constant to the right side:
\(x=0+3\)
- step4: Remove 0:
\(x=3\)
The equation \(x^{2}-6x+9=0\) has one root, which is \(x=3\).
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Simplify this solution Beyond the Answer
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!
