Question

1. $3x^2 - 9x + 6 = 0$

Explanation:

Step1: Simplify the equation

Divide the entire equation \(3x^{2}-9x + 6=0\) by 3. We get \(x^{2}-3x + 2=0\).

Step2: Factor the quadratic

We need to find two numbers that multiply to 2 and add up to - 3. The numbers are -1 and -2. So, \(x^{2}-3x + 2=(x - 1)(x - 2)=0\).

Step3: Solve for x

Set each factor equal to zero:

• For \(x - 1=0\), we get \(x = 1\).
• For \(x - 2=0\), we get \(x = 2\).

Answer:

The solutions of the equation \(3x^{2}-9x + 6 = 0\) are \(x = 1\) and \(x = 2\).