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punjab-curriculum-and-textbook-board-pctb
10th-class
mathematics
Mathematics 10
Linear and Quadratic Inequalities
Solving Quadratic Inequalities
Topic 4.2
3 mins read
hard Level
2024 Edition
Solving Quadratic Inequalities
Textbook Content
Formulas & Equations (4)
Solving Quadratic Inequalities
Example:
Find the solution set of
x
2
+
6
x
−
27
≤
0
x^{2} + 6x - 27\leq 0
x
2
+
6
x
−
27
≤
0
x
2
+
6
x
−
27
≤
0
x^{2} + 6x - 27\leq 0
x
2
+
6
x
−
27
≤
0
⇒
x
2
+
9
x
−
3
x
−
27
≤
0
⇒
x
2
+
9
x
−
3
x
−
27
≤
0
\Rightarrow x^{2} + 9x - 3x - 27\leq 0
⇒
x
2
+
9
x
−
3
x
−
27
≤
0
⇒
x
2
+
9
x
−
3
x
−
27
≤
0
x
(
x
+
9
)
−
3
(
x
+
9
)
≤
0
x(x + 9) - 3(x + 9)\leq 0
x
(
x
+
9
)
−
3
(
x
+
9
)
≤
0
⇒
(
x
+
9
)
(
x
−
3
)
≤
0
⇒
(
x
+
9
)
(
x
−
3
)
≤
0
\Rightarrow (x + 9)(x - 3)\leq 0
⇒
(
x
+
9
)
(
x
−
3
)
≤
0
⇒
(
x
+
9
)
(
x
−
3
)
≤
0
Topic Tags:
#quadratic inequalities
#solving inequalities
#mathematics
#10th class
Properties of Inequalities and Solving Linear Inequalities
Solving Systems of Linear Inequalities