Is there an easy way of remembering the quadratic formula?

2 Answers
May 3, 2018

Answer:

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!

May 3, 2018

Answer:

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)#