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

4237 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Integrate f(x) = 1/(1-x^2)


How do you calculate the cross product of two vectors?


Write down the equations of the three asymptotes and the coordinates of the points where the curve y = (3x+2)(x-3)/(x-2)(x+1) crosses the axes.


By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)


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