Quadratic with zeros -2 and 5

Step by step

The question

Question: write a quadratic with zeros −2 and 5.

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 −2 gives x − (−2).

Minus a minus is plus: x + 2.

Next, 5 gives x − 5.

Careful!

The sign flips.

The zero −2 gives x + 2, because that is 0 when x is −2.

2 Write f(x)

So f(x) = (x + 2)(x − 5).

3 Multiply out

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

(x + 2) times (x − 5).

Each part times each part.

Like terms together: x² − 3x − 10.

So f(x) = x² − 3x − 10.

4 Check

Let's check: put each zero in.

First x = −2.

We get 0.

And x = 5.

We get 0.

Let's look back.

First: each zero gives a bracket.

Then: write f(x).

Then: multiply out.

Last: check.