Is there an easy way of remembering the quadratic formula?
2 Answers
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!
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
Given:
#ax^2+bx+c = 0" "# with# \ a != 0#
Multiply by
#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
#x = (-b+-sqrt(b^2-4ac))/(2a)#