The complex conjugate of 2-3i is also a root of z^3+pz^2+qz-13p=0. Find a quadratic factor of z^3+pz^2+qz-13p=0 with real coefficients and thus find the real root of the equation.
z-2+3i times z-2-3i = z2-4z+13. z3-2z2+5z+26 divided by z2-4z+13 = z+2. Therefore the real root is z=-2.
WN
Related Maths A Level answers
All answers ▸Differentiate y=(x^2+1)(e^-x)
Why is it that sin^2(x) + cos^2(x) = 1?
Find the volume of revolution when the curve defined by y=xe^(2x) is rotated 2*pi radians about the x-axis between x=0 and x=1
Express (16x^2 + 4x^3)/(x^3 + 2x^2 - 8x) + 12x/(x-2) as one fraction in its simplest form.