Express x^2 - 7x + 2 in the form (x - p)^2 + q , where p and q are rational numbers.

This is an example of completing the square.If we expand (x - p)^2 + q, we will have x^2 -2px + p + q.Now we can use algebra to work out what p and q are from the following equation. x^2 - 7x + 2 = x^2 -2px + p^2 + q -7x + 2 = -2px + p^2 + q We can force an answer because 7x must equal to -2px so p = 7/2. Put p into the equation to get q. 7x + 2 = -27/2x + (7/2)^2 + q q = -41/4 so (x - 7/2)^2 -41/4

CP
Answered by Catherine P. Maths tutor

18634 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you form a Cartesian equation from two parametric equations?


What are complex numbers?


Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]


Can you prove to me why cos^2(X) + sin^2(X) = 1?


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