x² – 5x + 6=0 (Step by Step Solution)

Question: Solve \(x^2 – 5x + 6 = 0\). Step by step solution

Short Answer: The roots of the quadratic equation are x = 2 and x = 3.

Step by Step Solution

1. Write the equation: \(x^2 – 5x + 6 = 0\).
2. Factorize: find two numbers that multiply to 6 and add to -5. They are -2 and -3.
3. So, \(x^2 – 5x + 6 = (x – 2)(x – 3)\).
4. Set each factor equal to 0: \(x – 2 = 0 \Rightarrow x = 2\), and \(x – 3 = 0 \Rightarrow x = 3\).

Alternative Method: Quadratic Formula

Using the formula \(x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\) with \(a=1, b=-5, c=6\):

\(x = \frac{5 \pm \sqrt{(-5)^2 – 4(1)(6)}}{2}\) \(= \frac{5 \pm \sqrt{25 – 24}}{2}\) \(= \frac{5 \pm 1}{2}\).

So, the roots are x = 2 and x = 3.

Final Answer

The solutions are x = 2 and x = 3.

Practice More

• Solve \(x^2 – 7x – 12 = 0\)
• Quadratic Word Problems with Solutions