How do I write the function in standard form f(x) -5 and -4i

Question

F(x) has roots of -5 and -4i. It is also know that f(0) =-240

Answer 1

Hi Jes;

 

f(x) has a root at -5 so (x+5) is a factor

f(x) has a root at -4i so (x-(-4i)) or (x+4i) is a factor

If -4i is a factor, then so is the complex conjugate 4i, so

(x-4i) is a factor

 

The polynomial is:

f(x) = a(x+5)(x+4i)(x-4i)

f(x) = a(x+5)(x² + 16)

f(x) = a(x³ + 5x² + 16x + 80)

 

f(0) = -240 so

a(80) = -240

a = -3

 

Your polynomial is:

 

f(x) = -3(x³ + 5x² +16x + 80) = -3x³ - 15x² - 48x - 240

 

Questions?