Show how to derive the quadratic formula

You have a general quadratic of the form: ax^2 + bx + c = 0, where a,b,c are constants (although is consistent for functions). Divide by a (assuming a/=0, this would not be a quadratic in that case):x^2 + (b/a)x + c/a = 0Complete the square on the first 2 terms:(x+(b/2a))^2 - (b/2a)^2Add the 3rd term back on:(x+(b/2a))^2 - (b/2a)^2 + c/a = 0Rearrange to have the x term on its own:(x+(b/2a))^2 = (b/2a)^2 - c/aTake the square root:x+(b/2a) = +/-sqrt{(b/2a)^2 - c/a}Subtract b/2a:x = -b/2a +/- sqrt{(b/2a)^2 - c/a}Putting the right hand side over a common denominator:x = [-b +/- sqrt{b^2-4ac}]/2a

TF
Answered by Tom F. Maths tutor

3034 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the area under a curve between two points?


Find the gradient of the curve y = sin(2x) + 3 at the point where x = pi


What does a 95% confidence interval reflect?


A 1kg mass is launched from the ground into the air at an angle of 30 degrees to the horizontal and with initial speed 25 ms^-1. Assuming negligible air resistance, how far from the starting point will the mass travel before it hits the ground?


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