Given that the equation x^2 - 2x + 2 = 0 has roots A and B, find the values A + B, and A * B.

There are two obvious approaches here:
1. Solve the equation x2 - 2x + 2 = 0 to find A and B and then calculate the required values.

2. Or we can use the quicker method of analysing what it means for the expression to have these two roots.

It implies that the expression on the left hand side can be factorised into the form (x - A) (x - B) as this provides the solutions x = A, x = B to the equation (x - A) (x - B) = 0. Expanding this out in general gives x2 - (A + B) x + A * B = 0.

By comparing the two equations we can then read off from the coefficients that - (A + B) = - 2 and A * B = 2. So we now have the answers:

A + B = 2
A * B = 2

SP
Answered by Srijan P. Further Mathematics tutor

4295 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi


Express the complex number (1+i)/(1-i) in the form x+iy


By Differentiating from first principles, find the gradient of the curve f(x) = x^2 at the point where x = 2


How do you invert a 2x2 matrix?


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