PART - 1 CH - 5 Linear Inequalities — Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceMathsPART - 1 CH - 5 Linear Inequalities2 Marks
Question
Write the solution of inequality $x^2-4 x+3 \geq 0$.
✓
Answer
$\begin{array}{l}x^2-4 x+3 \geq 0 \\\Rightarrow \quad(x-3)(x-1) \geq 0\end{array}$ Hence, two following cases are possible : (i) $x-3 \geq 0$ and $x-1 \geq 0$ (ii) $x-3 \leq 0$ and $x-1 \leq 0$ $\text {for case (i)}\quad x-3 \geq 0 \Rightarrow x \geq 3$ $\text {and}\quad x-1 \geq 1 \Rightarrow x \geq 1$ So the possible solution of above case is $x \geq 3$ Hence, the required solution of given inequality. $\begin{array}{l}x \geq 3 \text { and } x \leq 1 \\ (-\infty, 1] \cup[3, \infty)\end{array}$
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