# Functions and algebra: Solve algebraic equations and inequalities

### Subject outcome

Subject outcome 2.3: Solve algebraic equations and inequalities

### Learning outcomes

• Solve quadratic equations by means of:
• Factorisation
• Completing the square
• Solve simultaneous equations with two unknowns algebraically and graphically, where the one equation is linear and the other equation is quadratic.
• Solve quadratic inequalities in one variable and represent the solution in the following ways:
• In set builder notation
• Interval notation
• On the number line.

### Unit 1 outcomes

By the end of this unit you will be able to:

• Apply the zero-product law.
• Solve rational quadratic equations which have fractions with the unknown in the denominator.
• Factorise quadratic expressions to solve for the unknown variable.

### Unit 2 outcomes

By the end of this unit you will be able to:

• Solve a quadratic equation by completing the square.

### Unit 3 outcomes

By the end of this unit you will be able to:

• Understand when to use the quadratic formula to solve quadratic equations.
• Apply the quadratic formula when necessary.

### Unit 4 outcomes

By the end of this unit you will be able to:

• Solve simultaneous equations algebraically where the one equation is linear and the other equation is quadratic.
• Solve simultaneous equations graphically where the one equation is linear and the other equation is quadratic.

### Unit 5 outcomes

By the end of this unit you will be able to:

• Find the critical values.
• Solve quadratic inequalities using the table and graphical methods.
• Represent the solution using set builder notation, interval notation and on a number line.