Derive the quadratic formula (Hint: complete the square)

Firstly, the quadratic formula finds the roots of a quadratic equation. 
So this means f(x) = 0. A general polynomial with highest power 2 looks like: ax+ bx +c.
Usings the two facts we just stated, we solve for the roots of ax+ bx +c = 0. ax+ bx +c = 0
x+ (b/a)x + (c/a) = 0
USINGING THE HINT
(x + (b/2a))- (b/2a)2 + (c/a) = 0
(x + (b/2a))2 = (b/2a)2 -(c/a)  
Make the right hand side all one fraction
(x + (b/2a))2 = (b2/4a2) - (4ac/4a2)
(x + (b/2a))2 = (b2-4ac) / 4a2
Squareroot both sides
x + (b/2a) = (+/-) (b2-4ac)1/2 / 2a          (The (+/-) comes from the squareroot having 2 sol's. e.g 41/2 = 2 or -2)
x = (-b (+/-) (b2-4ac)1/2) / 2a

RK
Answered by Riu K. Maths tutor

3513 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The lines y = 3x² - x + 5/2 intersects the line y = x/2 +7 at two points. Give their coordinates. Show your working


Write 5x^2 + 30x + 36 in the form 5(x+A)^2+B where A and B are integers to be found.Then write the equation of symmetry for the graph of 5x^2 + 30x + 36


Find the stationary points of the curve y=2*x^3-15*x^2+24*x+17. Determine whether these points are maximum or minimum.


Solve the simultaneous equations: x+y =2; x^2 + 2y = 12


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences