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
5624 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Give the general solution to the Ordinary Differential Equation: (dy/dx) + 2y/x = 3x+2
The function f is defined for x > 0 by f (x) = x^1n x. Obtain an expression for f ′ (x).
A particle is undergoing circular motion in a horizontal circle, that lies within the smooth surface of a hemispherical bowl of radius 4r. Find the distance OC (explained in diagram) if the angular acceleration of the particle is equal to root (3g/8r).
Find the solution the the differential equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x)