Quadratic with zeros 3 and 4

Step by step

The question

Question: write a quadratic with zeros 3 and 4.

A zero of f is an x that makes f(x) equal 0.

1 Each zero gives a bracket

If c is a zero, then x minus c is a factor.

Put c in, and that bracket is 0, so all of f(x) is 0.

The zero 3 gives x − 3.

Next, 4 gives x − 4.

Careful!

The sign flips.

The zero 3 gives x − 3, because that is 0 when x is 3.

2 Write f(x)

So f(x) = (x − 3)(x − 4).

3 Multiply out

Each part of the first bracket times each part of the second.

(x − 3) times (x − 4).

Each part times each part.

Like terms together: x² − 7x + 12.

So f(x) = x² − 7x + 12.

4 Check

Let's check: put each zero in.

First x = 3.

We get 0.

And x = 4.

We get 0.

Let's look back.

First: each zero gives a bracket.

Then: write f(x).

Then: multiply out.

Last: check.