Question

Is there an easy way of remembering the quadratic formula?

Answer 1

Quick writing

Explanation:

Here's someone else's mnemonic:
From square of b, take 4ac;
Square root extract, and b subtract;
Divide by 2a; you’ve x, hooray!

Answer 2

Here's what I think is the best way...

Explanation:

The very best way to remember it is to learn how to derive it.

We will complete the square and use the difference of squares identity:

`A^2-B^2=(A-B)(A+B)`

with `A = 2ax+b` and `B = sqrt(b^2-4ac)`

Given:

`ax^2+bx+c = 0" "` with `\ a != 0`

Multiply by `4a` to get:

`0 = 4a^2x^2+4abx+4ac`

`color(white)(0) = (2ax)^2+2b(2ax)+4ac`

`color(white)(0) = (2ax)^2+2b(2ax)+b^2+4ac-b^2`

`color(white)(0) = (2ax+b)^2-(b^2-4ac)`

`color(white)(0) = (2ax+b)^2-(sqrt(b^2-4ac))^2`

`color(white)(0) = ((2ax+b)-sqrt(b^2-4ac))((2ax+b)+sqrt(b^2-4ac))`

`color(white)(0) = (2ax+b-sqrt(b^2-4ac))(2ax+b+sqrt(b^2-4ac))`

Hence:

`2ax = -b+-sqrt(b^2-4ac)`

Then dividing both sides by `2a`, we get:

`x = (-b+-sqrt(b^2-4ac))/(2a)`