Show that x^2 - x +2 is positive for all values of x

(x-1/2)= (x-1/2)(x-1/2)=x2-x+1/4, add 7/4 to get x2-x+2 therefore x2-x+2 = (x-1/2)2 + 7/4

squared numbers always positive so (x-1/2)2 >= 0 therefore (x-1/2)2 + 7/4 is always positive

Answered by Pearse M. Maths tutor

10529 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)


Find the exact solution, in its simplest form, to the equation ln(4y + 7) = 3 + ln(2 – y) (Core Maths 3 Style Question)


How do you find the coordinate of where two lines intersect?


Prove that (1-cos2x)/sin(2x) = tan(x) where x ≠ nπ/2


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