Complex numbers (1 Viewer)

[shady145]

consider the equation 2z^3 - 3z^2 + 18z + 10 = 0
i) Given that 1-3i is a root of the equation, explain why 1+3i is another root.

ii) Find all roots of the equation.

Could u show all reasoning and explain please. TY

 

[tommykins]

i) polynomial has real coefficients and therefore complex roots come in conjugate pairs.

ii) sum of roots = 3/2 = (1-3i)+(1+3i) + a = 2 + a

2+a = 3/2
a = -1/2

 

[alakazimmy]

i) polynomial has real coefficients and therefore complex roots come in conjugate pairs.

Otherwise known as the conjugate root thereom