Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions
x = i is a solution, and all the coefficients are real, so x = -i must also be a solution:2x^3+3x^2+2x+3 = 0(x+i)(x-i)(Ax+B) = 0 (we argued above that this must be the case)(x^2+1)(Ax+B) = 0(x^2+1)(2x+3) = 0 (we identify A and B by comparing to the first line)Therefore x = -3/2 is the third solution, and we have all the solutions
BS
Answered by Ben S. • Further Mathematics tutor
2571 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Find the general solution of the second order differential equation y''(t)+y(t) = 5exp(2t)
Find the inverse of a 3x3 matrix
Define tanh(t) in terms of exponentials
Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0