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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

Srijan P. A Level Maths tutor, GCSE Maths tutor, A Level Further Math...

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