Question

Find a cubic function that has the roots 5 and 3-2i

Answer 1

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.

Answer 2

Answer:

1 and 3 – 2i are the roots of cubic equation then this equation is :