This "Find a monic polynomial f(x) of least degree..." has been solved

Secondary
Algebra
Algebra II
Polynomial factorization

tebollahb Answered2022-01-14

Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a monic polynomial g(x) of least degree with real coefficients that has the given numbers as zeros. -3i, 4

Answer & Explanation

Esta Hurtado Expert2022-01-15Added 39 answers

Step 1 Given, Zeros, −3i,4 it has three zeros

\pm 3 i, 4

these zeros are factor of the equation
g(x)=(x-3i)(x+3i)(x-4)
now solve this equation

(x^{2} + 9) (x - 4) = 0

x^{3} - 4 x^{2} + 9 x - 36 = 0

so it is a cubic polynomial
Step 2
so polynomial is

x^{3} - 4 x^{2} + 9 x - 36 = 0

Do you have a similar question?

Recalculate according to your conditions!

Most Popular Questions

Aryanna Rowland

2022-03-16

What is the instantaneous rate of change of

f (x) = (x^{2} - 3 x) e^{x}

at x=2?

See answers (1)

Lizeth Herring

2022-12-30

If x varies directly as a square of y for y=6, x=72. Find x for y=9.

See answers (1)

talpajocotefnf3

2022-03-27

For what values of x is

f (x) = 2 x^{4} + 4 x^{3} + 2 x^{2} - 2

concave or convex?

See answers (1)

Didn't find what you were looking for?