Derive from the standard quadratic equation, the form of the quadratic solution

ax2+bx+c=0 : basic quadratic equation

a(x+ bx/a) + c=0  

a((x+b/2a)- b2/4a2) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b2/4a2, )

a(x+b/2a)2 - b2/4a + c= 0 (a cancels 4ato make 4a)

a(x+b/2a)2 = (b2-4ac)/4a  (rewrite b2/4a - c)

(x+b/2a)2 = (b2-4ac)/4a2

(x+b/2a) = +/-(rootof(b2-4ac))/2a  (square root gives +/- answers

x= (-b +/- (rootof(b2-4ac)))/2a  (x term singled out and the quadratic soln is written)

 

JD
Answered by Jaiveer D. Maths tutor

5880 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the ODE y' = -x/y.


By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .


Consider the function f (x) = (2/3) x^3 + bx^2 + 2x + 3, where b is some undetermined coefficient: (a) find f'(x) and f''(x) and (b) if you know that f(x) has a stationary point at x = 2, use this information to find b.


How do one tailed and two tailed hypothesis tests differ


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning