Please, expand the following double brackets:

=

Please, tell me if I have got the right answer. If not, write the right answer:

Please, expand the following double brackets:

Please, tell me if I have got the right answer. If not, write the right answer:

(the right answer is ) (OK) (the right answer is )

ANSWERS

Quadratic equationsObjective: at the end of this lesson you will be able • to factorize a quadratic expression

in two different brackets

(Level B for GCSE)• to solve a quadratic equation

(Level A for GCSE)

To factorize this quadratic expression

you need to find two numbers whose product is equal to

8and whose sum is equal to

-6

You can try, for example, with

8 and 1

Product:

Sum:

You can try with two other numbers

2 and 4

Product:

Sum:

You can try with two other numbers

-2 and -4

Product:

Sum:

So the two numbers are

-2 to -4

You can write the initial expression

as

which means

(𝑥+…)(𝑥+…)(𝑥+−2 )(𝑥+…)(𝑥+−2 )(𝑥+−4)

(𝑥−2 )(𝑥−4)

Let’s try with the quadratic expression

How much has to be the sum of the two numbers?

How much has to be the product of the two numbers?

Which are the two numbers?

Let’s try with the quadratic expression

How much has to be the sum of the two numbers?

How much has to be the product of the two numbers?

Which are the two numbers?

Let’s try with the quadratic expression

How much has to be the sum of the two numbers?

How much has to be the product of the two numbers?

Which are the two numbers?

Let’s try with the quadratic expression

How much has to be the sum of the two numbers?

How much has to be the product of the two numbers?

Which are the two numbers?

Worksheet

Please, factorize the following expressions:

Please, factorize the following expressions:

ANSWERS

To solve the following quadratic equation

you need, firstly, to factorize the quadratic expression

This expression is equal to

This quantity has to be equal to 0:

When a product is equal to 0?

When at least one of the two numbers is equal to 0.

So

means that

that is to say

These are the solutions of the quadratic equation.

Try to solve the quadratic equation

remembering that

You need to solve

that means

So the solution of the equation are

Solve the following quadratic equation:

Answer:

Solve the following quadratic equation:

Answer:

Solve the following quadratic equation:

Answer:

Solve the following quadratic equation:

Answer:

Solve the following quadratic equation:

Answer:

Game