How many solutions x^2 + 4x + 3 = 0 Step by Step

Step by step

The question

Question: find the number of real solutions of x² + 4x + 3 = 0.

x² + 4x + 3 = 0

1 Find a, b and c

We read the numbers: a = 1 is with x², b = 4 is with x, c = 3 is the plain number.

a = 1, b = 4, c = 3

2 Work out b² − 4ac

In the formula, b² − 4ac is under the square root.

It is called the discriminant.

Its sign tells us how many solutions there are.

x = −b ± √b² − 4ac2a

We put the numbers in, each negative one in brackets.

b² − 4ac = 4² − 4 × 1 × 3

4² is 16.

4 times 1 times 3 is 12.

4² = 4 × 4 = 16

4 × 1 × 3 = 12

Careful!

b is squared first: b² means 4 times 4, not 4.

Careful: not 4 − 12 ✗

So we have 16 take away 12.

= 16 − 12

So the discriminant is 4.

= 4

3 How many solutions

4 is positive.

The square root of a positive number is a real number.

The plus or minus gives two different answers.

positive → 2 real solutions

0 → 1 real solution

negative → no real solutions

So x² + 4x + 3 = 0 has 2 real solutions.

= 2 real solutions

4 Check

Let's check with the formula.

Under the root we get 4.

Its square root is 2.

x = −4 ± 22

The plus gives −1, the minus gives −3.

Two different solutions.

It works!

x = −1 or −3

Let's look back.

First: find a, b and c.

Then: work out b² − 4ac.

Then: how many solutions.

Last: check.

Answer