Solution:
Given:
[tex]f(x)=x^2-4x+3[/tex]
Factorizing the function;
[tex]\begin{gathered} x^2-4x+3=x^2-3x-x+3 \\ =x(x-3)-1(x-3) \\ =(x-1)(x-3) \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} x^2-4x+3\leq0 \\ (x-1)(x-3)\leq0 \end{gathered}[/tex]
To get the solution, it must satisfy the condition of the inequality given.
[tex]ab\leq0,\text{ }a\ge0,b\leq0[/tex]
Hence,
[tex]\begin{gathered} (x-1)(x-3)\leq0 \\ x-1\ge0,x-3\leq0 \\ x\ge1,x\leq3 \\ \\ Combining\text{ the two inequalities, the solution is;} \\ 1\leq x\leq3 \end{gathered}[/tex]
