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

18609 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the solutions to z^2 = i


How do I rationalise the denominator of a fraction which consists of surds?


Integrate a^x with respect to x


Find the two real roots of the equation x^4 - 5 = 4x^2 . Give the roots in an exact form. [4]


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