What's the proof for the quadratic formula?

Mathematics is a unique subject within which many equations that you encounter have lots of functions and can be derived from the basics. The quadratic formula for instance is incredibly useful to quickly solve quadratics (with real roots) that cannot be factorised: It seems at first very tricky indeed at the first glance on how to start, however it only requires GCSE knowledge for the proof; completing the square. We start with ax2+bx+c=0, where y=0 and the next steps follow: 1. Factorise out the 'a' a(x2+bx/a) +c=0. 2. Half the inside number&square the bracket&subtract square from inside to make the function equal to the previous line a[(x+b/2a)2-(b/2a)2] +c=0. 3. Expand the brackets a(x+b/2a)2-b2/4a +c=0. 4. Keep the 'x' term to one side a(x+b/2a)2. =b2/4a - c. 5. Combine the fractions a(x+b/2a)2 =(b2-4ac) /4a. 6. Divide by 'a' (x+b/2a)2 =(b2-4ac) /4a2 7. Square root both sides x+b/2a = √(b2-4ac) / 2a. 8. Make 'x' on its own by subtracting b/2a from both sides. Voila! x = [-b± √(b2-4ac)] / 2a.

AO
Answered by Azeem O. Maths tutor

4110 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Why does the constant disappear when differentiating a function?


Differentiate y= 8x^2 +4x +5


Find the solutions of the equation 3cos(2 theta) - 5cos(theta) + 2 = 0 in the interval 0 < theta < 2pi.


Solve the following equation, give the answer/answers as coordinates. y=3x^2 , y=2x+5.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences