Solving Quadratics

Maths: Edexcel IGCSE Higher, topic 2.4.1

Solving Quadratics

Quadratics have two solutions, remember to include both of them when answering a question.

x2 has two solutions

x² has two solutions

+5 and -5

+5 and -5

√5 is a solution

√5 is a solution

− √5 is also a solution

− √5 is also a solution

Factorising Quadratics

We can solve quadratics using factorisation. We get two solutions, one from each bracket.

Find pairs of numbers which multiply to give (-8)

Find pairs of numbers which multiply to give (-8)

Choose the pair which also adds to give 2

Choose the pair which also adds to give 2

These numbers multiply to give (-8) and add to give 2

These numbers multiply to give (-8) and add to give 2

Write these two numbers in the brackets

Write these two numbers in the brackets

We have now factorised the equation

We have now factorised the equation

One solution is when the first bracket 0

One solution is when the first bracket = 0

This gives x 2

This gives x = 2

The second solution is when the second bracket 0

The second solution is when the second bracket = 0

This gives x -4

This gives x = -4

These are the two solutions to the quadratic

These are the two solutions to the quadratic

Solving Quadratics - Quadratic Formula

We can solve any quadratic using the quadratic formula.

Quadratic formula

Quadratic formula

The quadratic formula can be used to find the solution to any quadratic equation ax² + bx + c = 0.

Test yourself on Solving Quadratics

Which of these equations has two solutions for x?
Which of these are solutions to the equation:
x² = 7
Which of these are solutions to the equation:
x² = 19
What are the solutions for the equation:
x² = 6
What are the solutions for the equation:
x² = 11

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