Question

Write the simplest polynomial function with the given roots 2i, square root of 3, and 4

Answer 1

Answer:

• y = (x - 4)(x + 2i)(x - 2i)(x + √3)(x - √3) Possible answer
• y = (x - 4)(x^2 + 4)(x^2 - 3)                    Possible answer

Step-by-step explanation:

The simplest answer is that 2i cannot be a lone root. It must have a twin that is - 2i

√3 has the same sort of rule. It cannot be a root all by itself. It also must have a twin, in this case -√3

So the answer must be

(x - 4)(x + 2i)(x - 2i)(x + √3)(x - √3)      <<< Possible answer

but this can be reduced even further.

• (x + 2i)(x - 2i) = x^2 - x*2i + x*2i - 4i^2
• (x + 2i)(x - 2i) = x^2 - 4(i)^2
• (x + 2i)(x - 2i) = x^2  + 4.               Remember i^2 = - 1

By a similar method (x - √3)(x + √3) = x^2 - 3

So the polynomial is reduced to

(x - 4)(x^2 + 4)(x^2 - 3)  <<<< Answer

If this is not among your answers and the  factored form is not either, please tell me what is.