Find a cubic function that has the roots 5 and 3-2i
Answers
Answered by
0
Answer:
x³-11x²+43x-65.
Step-by-step explanation:
We are required to find the cubic function that has the roots
5 and 3-2i.
Please note that 3-2i which is complex is a root of the cubic function.
Always , complex roots occurs in pairs i.e.,
If a+ ib is a root of the equation, then its complex conjugate
a - i b will also be a root of that equation.
Hence , given 3-2i is a root, so 3+2i also will be the root of the equation.
Hence we need to find the cubic whose roots are 5,3+2i,3-2i
If we know the zeros of the cubic as a, b and c then the cubic will be of the form
(x-a)(x-b)(x-c)
Hence the cubic is (x-5)(x-(3-2i))(x-(3+2i))
=(x-5)(x²-6x+13)
=x³-11x²+43x-65.
Answered by
0
Answer:
1 and 3 – 2i are the roots of cubic equation then this equation is :
Similar questions