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how to do the 1st question (part b c d are all basically same so please explain those to so i understand)

How To Do The 1st Question Part B C D Are All Basically Same So Please Explain Those To So I Understand class=

Sagot :

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]