Question

Create a polynomial with theese qualities:
Degree 4, 2 positive real zeros, 0 negative real zeros, 2 complex zeros.

Answer 1

its simply

P(x) = (x - 3)(x -2)(x -2i)(x + 2i)

real positive zeros 3, 2 complex zeros, -2i, 2i

Answer 2

you just need to expand it out

Answer 3

Thanks, but how exactly did you figure that out??

Answer 4

well start by distributing

(x -3)(x -2) =

and

(x -2i)(x+2i) =

which is the difference of 2 squares


then multiply the 2 answers

Answer 5

well its easy to figure out. I just chose some numbers

roots of polynomials are the values that make it zero



P(x) = (x + a)(x -b) the roots are -a and b

so if you are asked for real positive roots then it would be x = a, b

so the binomial factors are P(x) = (x -a)(x-b)

complex roots involve i because i^2 = -1

as an example

if P(x) = x^2 + 9 to find the zeros you have x^2 + 9 = 0

solving for x you get x^2 = -9 so using -1 = i^2

x^2 = 9i^2

now you can find roots at -3i and 3i

reallY i just chose random numbers that met the conditions.