2.3.3
Solving Quadratic Inequalities
Quadratic Inequalities
Quadratic Inequalities
Find inequalities for x when x² > 9 and for x² < 9:
![Illustrative background for x² > 9](https://image-v2.cdn.app.senecalearning.com/2018-04/135036eb-7310-42d2-bcb3-0321c0f8a95d/Screen%20Shot%202018-04-16%20at%2017.18.17,h_400,q_80,w_640.png)
![Illustrative background for x² > 9 ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-04/135036eb-7310-42d2-bcb3-0321c0f8a95d/Screen%20Shot%202018-04-16%20at%2017.18.17,h_400,q_80,w_640.png)
x² > 9
x² > 9
- Square root both sides.
- If x² is more than the answer, x must be smaller than the negative or larger than the positive.
![Illustrative background for x² < 9](https://image-v2.cdn.app.senecalearning.com/2018-04/ed3ac001-d631-48d3-b065-fcc63f8c26ba/Screen%20Shot%202018-04-16%20at%2017.18.13,h_400,q_80,w_640.png)
![Illustrative background for x² < 9 ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-04/ed3ac001-d631-48d3-b065-fcc63f8c26ba/Screen%20Shot%202018-04-16%20at%2017.18.13,h_400,q_80,w_640.png)
x² < 9
x² < 9
- Square root both sides.
- If x² is less than the answer, x must be in between the two values.
- A useful check is to see if x = 0 satisfies the inequality.
- If it does x must be in between the two square roots.
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
Jump to other topics
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
![Go student ad image](/en-GB/revision-notes/_next/image?url=%2Fen-GB%2Frevision-notes%2Fimages%2Fgo-student-uk-ad.jpg&w=640&q=100)
Unlock your full potential with GoStudent tutoring
Affordable 1:1 tutoring from the comfort of your home
Tutors are matched to your specific learning needs
30+ school subjects covered