2x^2-6x+5 can be written in the form a(x -b)^ 2 + c where a, b and c are positive numbers. Find a,b and c.

In order to solve this problem we must first complete the square. To complete the square we need to factorise the equation to get the coefficient of x to be 1. This gives: 2(x^2-3x)+5. We then need to complete the square for x^2-3x. This gives: 2((x-1.5)^2-(1.5)^2)+5=2((x-1.5)^2-2.25)+5. [When completing the square we need to half the coefficient of x and minus it from x^2, we then change the x^2 to x and square this. We then minus the value of the coefficient squared from the squared brackets.] We finally need to simplify: 2((x-1.5)^2-2.25)+5=2(x-1.5)^2-4.5+5=2(x-1.5)^2+0.5. So from the initial question this gives a=2, b=1.5, c=-0.5.

CH
Answered by Chloe H. Maths tutor

21135 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise X^2-X-20


The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.


Solve the following simultaneous equations: 4x + 5y = -8 and 6x-2y = 26


GCSE 2011: Solve the simultaneous equations: y^2 = 2x + 29 and y = x - 3


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