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

Related Further Mathematics A Level answers

All answers ▸

Solve the second order differential equation d^2y/dx^2 - 4dy/dx + 5y = 15cos(x), given that when x = 0, y = 1 and when x = 0, dy/dx = 0


a) Show that d/dx(arcsin x) = 1/(√ (1-x²)). b) Hence, use a suitable trigonometric substitution to find ∫ (1/(√ (4-2x-x²))) dx.


For f(x) = (3x+4)^(-2), find f'(x) and f''(x) and hence write down the Maclaurin series up to and including the term in x^2.


Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)


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